The Map of Math

MSC Classification Codes

The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme formulated by the American Mathematical Society. I am using it here to classify all the mathematics on this website.

General Math

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

• General reference works (handbooks, dictionaries, bibliographies, etc.)
• Instructional exposition (textbooks, tutorial papers, etc.)
• Research exposition (monographs, survey articles)
• Historical (must also be assigned at least one classification number from Section 01)
• Explicit machine computation and programs (not the theory of computation or programming)
• Proceedings, conferences, collections, etc.
• Ordered sets
• Total order
• Partial order, general
• Combinatorics of partially ordered sets
• Algebraic aspects of posets
• Semilattices
• Galois correspondences, closure operators
• None of the above, but in this section
• Lattices
• Structure theory
• Ideals, congruence relations
• Representation theory
• Varieties of lattices
• Complete lattices, completions
• Free lattices, projective lattices, word problems
• Topological lattices, order topologies
• Continuous lattices and posets, applications
• None of the above, but in this section
• Modular lattices, complemented lattices
• Modular lattices, Desarguesian lattices
• Semimodular lattices, geometric lattices
• Complemented lattices, orthocomplemented lattices and posets
• Complemented modular lattices, continuous geometries
• None of the above, but in this section
• Distributive lattices
• Structure and representation theory
• Complete distributivity
• Pseudocomplemented lattices
• Heyting algebras
• Frames, locales
• Post algebras
• De Morgan algebras, Lukasiewicz algebras
• MV-algebras
• Lattices and duality
• Fuzzy lattices (soft algebras) and related topics
• None of the above, but in this section
• Boolean algebras (Boolean rings)
• Structure theory
• Chain conditions, complete algebras
• Stone space and related constructions
• Ring-theoretic properties
• Boolean algebras with additional operations (diagonalizable algebras, etc.)
• Boolean functions
• None of the above, but in this section
• Ordered structures
• Ordered semigroups and monoids
• Quantales
• Noether lattices
• Ordered groups
• Ordered abelian groups, Riesz groups, ordered linear spaces
• Ordered rings, algebras, modules
• Topological lattices, order topologies
• BCK-algebras, BCI-algebras
• None of the above, but in this section

General algebraic systems

• General reference works (handbooks, dictionaries, bibliographies, etc.)
• Instructional exposition (textbooks, tutorial papers, etc.)
• Research exposition (monographs, survey articles)
• Historical (must also be assigned at least one classification number from Section 01)
• Explicit machine computation and programs (not the theory of computation or programming)
• Proceedings, conferences, collections, etc.
• Algebraic structures
• Relational systems, laws of composition
• Structure theory
• Subalgebras, congruence relations
• Automorphisms, endomorphisms
• Operations, polynomials, primal algebras
• Equational compactness
• Word problems
• Partial algebras
• Unary algebras
• Finitary algebras
• Infinitary algebras
• Heterogeneous algebras
• Applications of universal algebra in computer science
• Fuzzy algebraic structures
• None of the above, but in this section
• Varieties
• Equational logic, Malcev (Maltsev) conditions
• Congruence modularity, congruence distributivity
• Lattices of varieties
• Free algebras
• Products, amalgamated products, and other kinds of limits and colimits
• Subdirect products and subdirect irreducibility
• Injectives, projectives
• None of the above, but in this section
• Other classes of algebras
• Categories of algebras
• Axiomatic model classes
• Quasivarieties
• None of the above, but in this section

Number theory

• General reference works (handbooks, dictionaries, bibliographies, etc.)
• Instructional exposition (textbooks, tutorial papers, etc.)
• Research exposition (monographs, survey articles)
• Historical (must also be assigned at least one classification number from Section 01)
• Explicit machine computation and programs (not the theory of computation or programming)
• Proceedings, conferences, collections, etc.
• Elementary number theory
• Multiplicative structure; Euclidean algorithm; greatest common divisors
• Congruences; primitive roots; residue systems
• Power residues, reciprocity
• Arithmetic functions; related numbers; inversion formulas
• Primes
• Factorization; primality
• Continued fractions
• Radix representation; digital problems
• Other representations
• None of the above, but in this section
• Sequences and sets
• Density, gaps, topology
• Additive bases
• Arithmetic progressions
• Representation functions
• Recurrences
• Fibonacci and Lucas numbers and polynomials and generalizations
• Sequences (mod $m$)
• [Farey sequences; the sequences 1^k, 2^k, cdots]$](11b57.md “MISSING PAGE”) Binomial coefficients; factorials; $q$-identities Bernoulli and Euler numbers and polynomials Bell and Stirling numbers Other combinatorial number theory Special sequences and polynomials Automata sequences None of the above, but in this section Polynomials and matrices Polynomials Matrices, determinants None of the above, but in this section Diophantine equations Linear equations Quadratic and bilinear equations Cubic and quartic equations Higher degree equations; Fermat’s equation Counting solutions of Diophantine equations Multiplicative and norm form equations Thue-Mahler equations Exponential equations Rational numbers as sums of fractions Equations in many variables Diophantine inequalities Congruences in many variables Representation problems $p$-adic and power series fields None of the above, but in this section Forms and linear algebraic groups Quadratic forms over general fields Quadratic forms over local rings and fields Forms over real fields Quadratic forms over global rings and fields General binary quadratic forms General ternary and quaternary quadratic forms; forms of more than two variables Sums of squares and representations by other particular quadratic forms Bilinear and Hermitian forms Class numbers of quadratic and Hermitian forms Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) Classical groups $K$-theory of quadratic and Hermitian forms Galois cohomology of linear algebraic groups Forms of degree higher than two Algebraic theory of quadratic forms; Witt groups and rings Quadratic spaces; Clifford algebras $p$-adic theory None of the above, but in this section Discontinuous groups and automorphic forms Modular and automorphic functions Structure of modular groups and generalizations; arithmetic groups Modular forms, one variable Automorphic forms, one variable Dedekind eta function, Dedekind sums Relationship to Lie algebras and finite simple groups Relations with algebraic geometry and topology Hecke-Petersson operators, differential operators (one variable) Theta series; Weil representation Fourier coefficients of automorphic forms Modular correspondences, etc. Congruences for modular and $p$-adic modular forms Forms of half-integer weight; nonholomorphic modular forms Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces Siegel modular groups and their modular and automorphic forms Jacobi forms Modular forms associated to Drinfel’d modules Other groups and their modular and automorphic forms (several variables) Hecke-Petersson operators, differential operators (several variables) Dirichlet series and functional equations in connection with modular forms Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols Representation-theoretic methods; automorphic representations over local and global fields Spectral theory; Selberg trace formula Cohomology of arithmetic groups Galois representations $p$-adic theory, local fields None of the above, but in this section Arithmetic algebraic geometry (Diophantine geometry) Elliptic curves over global fields Elliptic curves over local fields Drinfeld modules; higher-dimensional motives, etc. Abelian varieties of dimension $gtr 1$ Complex multiplication and moduli of abelian varieties Elliptic and modular units Arithmetic aspects of modular and Shimura varieties Curves over finite and local fields Varieties over finite and local fields Curves of arbitrary genus or genus $ne 1$ over global fields Varieties over global fields $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture Geometric class field theory Heights Polylogarithms and relations with $K$-theory None of the above, but in this section Geometry of numbers Lattices and convex bodies Nonconvex bodies Lattice packing and covering Products of linear forms Minima of forms Quadratic forms (reduction theory, extreme forms, etc.) Automorphism groups of lattices Mean value and transfer theorems Relations with coding theory None of the above, but in this section Diophantine approximation, transcendental number theory Homogeneous approximation to one number Markov and Lagrange spectra and generalizations Simultaneous homogeneous approximation, linear forms Approximation by numbers from a fixed field Inhomogeneous linear forms Diophantine inequalities Small fractional parts of polynomials and generalizations Approximation in non-Archimedean valuations Approximation to algebraic numbers Continued fractions and generalizations Distribution modulo one Irrationality; linear independence over a field Transcendence (general theory) Measures of irrationality and of transcendence Metric theory Algebraic independence; Gelfond’s method Linear forms in logarithms; Baker’s method Transcendence theory of elliptic and abelian functions Transcendence theory of other special functions Transcendence theory of Drinfel’d and $t$-modules Results involving abelian varieties Analogues of methods in Nevanlinna theory (work of Vojta et al.) None of the above, but in this section Probabilistic theory: distribution modulo $1$; metric theory of algorithms General theory of distribution modulo $1$ Normal numbers, radix expansions, etc. Special sequences Well-distributed sequences and other variations Irregularities of distribution, discrepancy Continuous, $p$-adic and abstract analogues Pseudo-random numbers; Monte Carlo methods Metric theory of continued fractions Metric theory of other algorithms and expansions; measure and Hausdorff dimension Diophantine approximation Arithmetic functions Harmonic analysis and almost periodicity None of the above, but in this section Exponential sums and character sums Trigonometric and exponential sums, general Gauss and Kloosterman sums; generalizations Estimates on exponential sums Jacobsthal and Brewer sums; other complete character sums Weyl sums Sums over primes Sums over arbitrary intervals Estimates on character sums None of the above, but in this section Zeta and $L$-functions: analytic theory $zeta (s)$ and $L(s, chi)$ Real zeros of $L(s, chi)$; results on $L(1, chi)$ Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses Hurwitz and Lerch zeta functions Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas Zeta and $L$-functions in characteristic $p$ Other Dirichlet series and zeta functions Tauberian theorems None of the above, but in this section Multiplicative number theory Distribution of primes Primes in progressions Distribution of integers with specified multiplicative constraints Turán theory Primes represented by polynomials; other multiplicative structure of polynomial values Sieves Applications of sieve methods Asymptotic results on arithmetic functions Asymptotic results on counting functions for algebraic and topological structures Rate of growth of arithmetic functions Distribution functions associated with additive and positive multiplicative functions Other results on the distribution of values or the characterization of arithmetic functions Distribution of integers in special residue classes Applications of automorphic functions and forms to multiplicative problems Generalized primes and integers None of the above, but in this section Additive number theory; partitions Waring’s problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method Inverse problems of additive number theory Elementary theory of partitions Analytic theory of partitions Partitions; congruences and congruential restrictions None of the above, but in this section Algebraic number theory: global fields Algebraic numbers; rings of algebraic integers PV-numbers and generalizations; other special algebraic numbers Polynomials (irreducibility, etc.) Quadratic extensions Cubic and quartic extensions Cyclotomic extensions Other abelian and metabelian extensions Other number fields Iwasawa theory Units and factorization Class numbers, class groups, discriminants Galois theory Integral representations related to algebraic numbers; Galois module structure of rings of integers Galois cohomology Class field theory Langlands-Weil conjectures, nonabelian class field theory Zeta functions and $L$-functions of number fields Distribution of prime ideals Density theorems Other analytic theory Quaternion and other division algebras: arithmetic, zeta functions Other algebras and orders, and their zeta and $L$-functions Adèle rings and groups Arithmetic theory of algebraic function fields Cyclotomic function fields (class groups, Bernoulli objects, etc.) Class groups and Picard groups of orders $K$-theory of global fields Totally real and totally positive fields None of the above, but in this section Algebraic number theory: local and $p$-adic fields Polynomials Ramification and extension theory Galois theory Integral representations Galois cohomology Class field theory; $p$-adic formal groups Langlands-Weil conjectures, nonabelian class field theory Zeta functions and $L$-functions Algebras and orders, and their zeta functions $K$-theory of local fields Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.) Other nonanalytic theory Prehomogeneous vector spaces None of the above, but in this section Finite fields and commutative rings (number-theoretic aspects) Polynomials Cyclotomy Exponential sums Other character sums and Gauss sums Structure theory Arithmetic theory of polynomial rings over finite fields Finite upper half-planes Algebraic coding theory; cryptography None of the above, but in this section Connections with logic Decidability Ultraproducts Model theory Nonstandard arithmetic None of the above, but in this section Computational number theory Factorization Primality Algorithms; complexity Analytic computations Algebraic number theory computations Computer solution of Diophantine equations Calculation of integer sequences Evaluation of constants Continued fraction calculations Values of arithmetic functions; tables None of the above, but in this section Miscellaneous applications of number theory

• Field theory and polynomials

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Real and complex fields
    • Polynomials: factorization
    • Polynomials: location of zeros (algebraic theorems)
    • Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
    • None of the above, but in this section
    • General field theory
    • Polynomials (irreducibility, etc.)
    • Special polynomials
    • Equations
    • Skew fields, division rings
    • Finite fields (field-theoretic aspects)
    • Hilbertian fields; Hilbert’s irreducibility theorem
    • Field arithmetic
    • None of the above, but in this section
    • Field extensions
    • Algebraic extensions
    • Separable extensions, Galois theory
    • Inverse Galois theory
    • Inseparable extensions
    • Transcendental extensions
    • None of the above, but in this section
    • Homological methods (field theory)
    • Galois cohomology
    • Cohomological dimension
    • None of the above, but in this section
    • Differential and difference algebra
    • Differential algebra
    • Difference algebra
    • Abstract differential equations
    • $p$-adic differential equations
    • None of the above, but in this section
    • Topological fields
    • Normed fields
    • Valued fields
    • Formally $p$-adic fields
    • Ordered fields
    • Topological semifields
    • General valuation theory
    • Non-Archimedean valued fields
    • Krasner-Tate algebras
    • None of the above, but in this section
    • Generalizations of fields
    • Near-fields
    • Semifields
    • None of the above, but in this section
    • Connections with logic
    • Decidability
    • Ultraproducts
    • Model theory
    • Nonstandard arithmetic
    • None of the above, but in this section
    • Computational aspects of field theory and polynomials

• Commutative rings and algebras

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • General commutative ring theory
    • Graded rings
    • Divisibility
    • Radical theory
    • Ideals; multiplicative ideal theory
    • Valuations and their generalizations
    • Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
    • Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure
    • Actions of groups on commutative rings; invariant theory
    • None of the above, but in this section
    • Ring extensions and related topics
    • Extension theory
    • Galois theory
    • Morphisms
    • Integral dependence
    • Integral closure of rings and ideals; integrally closed rings, related rings (Japanese, etc.)
    • Going up; going down; going between
    • Polynomials over commutative rings
    • Quotients and localization
    • Completion
    • Étale and flat extensions; Henselization; Artin approximation
    • None of the above, but in this section
    • Theory of modules and ideals
    • Structure, classification theorems
    • Projective and free modules and ideals
    • Injective and flat modules and ideals
    • Torsion modules and ideals
    • Other special types
    • Cohen-Macaulay modules
    • Dimension theory, depth, related rings (catenary, etc.)
    • Class groups
    • Linkage, complete intersections and determinantal ideals
    • None of the above, but in this section
    • Homological methods
    • Syzygies and resolutions
    • (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
    • Homological dimension
    • Homological functors on modules (Tor, Ext, etc.)
    • Deformations and infinitesimal methods
    • Grothendieck groups, $K$-theory
    • Homological conjectures (intersection theorems)
    • Complexes
    • Torsion theory
    • Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
    • Local cohomology
    • None of the above, but in this section
    • Chain conditions, finiteness conditions
    • Noetherian rings and modules
    • Artinian rings and modules, finite-dimensional algebras
    • Rings and modules of finite generation or presentation; number of generators
    • None of the above, but in this section
    • Arithmetic rings and other special rings
    • Dedekind, Prüfer and Krull rings and their generalizations
    • Euclidean rings and generalizations
    • Principal ideal rings
    • Factorial rings, unique factorization domains
    • Polynomial rings and ideals; rings of integer-valued polynomials
    • Formal power series rings
    • Valuation rings
    • Excellent rings
    • Seminormal rings
    • Rings with straightening laws, Hodge algebras
    • Face and Stanley-Reisner rings; simplicial complexes
    • None of the above, but in this section
    • Integral domains
    • Local rings and semilocal rings
    • Regular local rings
    • Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
    • Multiplicity theory and related topics
    • None of the above, but in this section
    • Topological rings and modules
    • Power series rings
    • Analytical algebras and rings
    • Complete rings, completion
    • Henselian rings
    • Global topological rings
    • Ordered rings
    • Real algebra
    • None of the above, but in this section
    • Witt vectors and related rings
    • Applications of logic to commutative algebra
    • Finite commutative rings
    • Structure
    • Polynomials
    • None of the above, but in this section
    • Differential algebra
    • Modules of differentials
    • Rings of differential operators and their modules
    • Derivations
    • None of the above, but in this section
    • Computational aspects of commutative algebra
    • Polynomials, factorization
    • Polynomial ideals, Gröbner bases
    • None of the above, but in this section

• Algebraic geometry

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Foundations
    • Relevant commutative algebra
    • Varieties and morphisms
    • Schemes and morphisms
    • Generalizations (algebraic spaces, stacks)
    • Noncommutative algebraic geometry
    • Elementary questions
    • None of the above, but in this section
    • Local theory
    • Singularities
    • Deformations of singularities
    • Infinitesimal methods
    • Local deformation theory, Artin approximation, etc.
    • Local cohomology
    • Formal neighborhoods
    • Local structure of morphisms: étale, flat, etc.
    • None of the above, but in this section
    • Cycles and subschemes
    • Parametrization (Chow and Hilbert schemes)
    • Chow groups and rings
    • Intersection theory, characteristic classes, intersection multiplicities
    • Divisors, linear systems, invertible sheaves
    • Pencils, nets, webs
    • Picard groups
    • Algebraic cycles
    • Transcendental methods, Hodge theory, Hodge conjecture
    • Torelli problem
    • Applications of methods of algebraic $K$-theory
    • Riemann-Roch theorems
    • None of the above, but in this section
    • Families, fibrations
    • Structure of families (Picard-Lefschetz, monodromy, etc.)
    • Fibrations, degenerations
    • Variation of Hodge structures
    • Arithmetic ground fields (finite, local, global)
    • Formal methods; deformations
    • Algebraic moduli problems, moduli of vector bundles
    • Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
    • Fine and coarse moduli spaces
    • None of the above, but in this section
    • Birational geometry
    • Rational and birational maps
    • Birational automorphisms, Cremona group and generalizations
    • Rationality questions
    • Global theory and resolution of singularities
    • Coverings
    • Ramification problems
    • Embeddings
    • Minimal model program (Mori theory, extremal rays)
    • None of the above, but in this section
    • (Co)homology theory
    • Vector bundles, sheaves, related constructions
    • Differentials and other special sheaves
    • Vanishing theorems
    • Étale and other Grothendieck topologies and cohomologies
    • Brauer groups of schemes
    • Classical real and complex cohomology
    • $p$-adic cohomology, crystalline cohomology
    • Homotopy theory; fundamental groups
    • de Rham cohomology
    • Motivic cohomology
    • Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
    • Topological properties
    • None of the above, but in this section
    • Arithmetic problems. Diophantine geometry
    • Rational points
    • Zeta-functions and related questions(Birch-Swinnerton-Dyer conjecture)
    • Finite ground fields
    • Local ground fields
    • Rigid analytic geometry
    • Global ground fields
    • Other nonalgebraically closed ground fields
    • Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
    • Modular and Shimura varieties
    • Arithmetic varieties and schemes; Arakelov theory; heights
    • Applications to coding theory and cryptography
    • None of the above, but in this section
    • Curves
    • Algebraic functions; function fields
    • Families, moduli (algebraic)
    • Families, moduli (analytic)
    • Singularities, local rings
    • Arithmetic ground fields
    • Coverings, fundamental group
    • Automorphisms
    • Jacobians, Prym varieties
    • Theta functions; Schottky problem
    • Special curves and curves of low genus
    • Plane and space curves
    • Special divisors (gonality, Brill-Noether theory)
    • Elliptic curves
    • Riemann surfaces; Weierstrass points; gap sequences
    • Vector bundles on curves and their moduli
    • Relationships with integrable systems
    • Relationships with physics
    • None of the above, but in this section
    • Surfaces and higher-dimensional varieties
    • Families, moduli, classification: algebraic theory
    • Moduli, classification: analytic theory; relations with modular forms
    • Singularities
    • Arithmetic ground fields
    • Special surfaces
    • Rational and ruled surfaces
    • Elliptic surfaces
    • $K3$ surfaces and Enriques surfaces
    • Surfaces of general type
    • $3$-folds
    • Calabi-Yau manifolds, mirror symmetry
    • $4$-folds
    • $n$-folds ($n>4$)
    • Fano varieties
    • Automorphisms of surfaces and higher-dimensional varieties
    • Vector bundles on surfaces and higher-dimensional varieties, and their moduli
    • Hypersurfaces
    • Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
    • Relationships with physics
    • None of the above, but in this section
    • Abelian varieties and schemes
    • Isogeny
    • Algebraic theory
    • Algebraic moduli, classification
    • Subvarieties
    • Arithmetic ground fields
    • Analytic theory; abelian integrals and differentials
    • Complex multiplication
    • Theta functions
    • Picard schemes, higher Jacobians
    • None of the above, but in this section
    • Algebraic groups
    • Formal groups, $p$-divisible groups
    • Group varieties
    • Group schemes
    • Affine algebraic groups, hyperalgebra constructions
    • Geometric invariant theory
    • Group actions on varieties or schemes (quotients)
    • Classical groups (geometric aspects)
    • Other algebraic groups (geometric aspects)
    • None of the above, but in this section
    • Special varieties
    • Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
    • Linkage
    • Low codimension problems
    • Complete intersections
    • Determinantal varieties
    • Grassmannians, Schubert varieties, flag manifolds
    • Homogeneous spaces and generalizations
    • Rational and unirational varieties
    • Toric varieties, Newton polyhedra
    • Supervarieties
    • None of the above, but in this section
    • Projective and enumerative geometry
    • Projective techniques
    • Enumerative problems (combinatorial problems)
    • Classical problems, Schubert calculus
    • Configurations of linear subspaces
    • Varieties of low degree
    • Adjunction problems
    • Gromov-Witten invariants, quantum cohomology
    • None of the above, but in this section
    • Real algebraic and real analytic geometry
    • Real algebraic sets
    • Semialgebraic sets and related spaces
    • Real analytic and semianalytic sets
    • Nash functions and manifolds
    • Topology of real algebraic varieties
    • None of the above, but in this section
    • Computational aspects in algebraic geometry
    • Curves
    • Surfaces, hypersurfaces
    • Higher-dimensional varieties
    • Effectivity
    • None of the above, but in this section
    • Affine geometry
    • Classification of affine varieties
    • Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
    • Jacobian problem
    • Group actions on affine varieties
    • Affine fibrations
    • None of the above, but in this section

• Linear and multilinear algebra; matrix theory

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Vector spaces, linear dependence, rank
    • Linear transformations, semilinear transformations
    • Linear equations
    • Matrix inversion, generalized inverses
    • Conditioning of matrices
    • Determinants, permanents, other special matrix functions
    • Eigenvalues, singular values, and eigenvectors
    • Canonical forms, reductions, classification
    • Matrix pencils
    • Factorization of matrices
    • Matrix equations and identities
    • Commutativity
    • Inverse problems
    • Algebraic systems of matrices
    • Matrices over special rings (quaternions, finite fields, etc.)
    • Matrices of integers
    • Linear inequalities
    • Inequalities involving eigenvalues and eigenvectors
    • Miscellaneous inequalities involving matrices
    • Positive matrices and their generalizations; cones of matrices
    • Stochastic matrices
    • Random matrices
    • Matrices over function rings in one or more variables
    • Other types of matrices (Hermitian, skew-Hermitian, etc.)
    • Norms of matrices, numerical range, applications of functional analysis to matrix theory
    • Quadratic and bilinear forms, inner products
    • Clifford algebras, spinors
    • Multilinear algebra, tensor products
    • Vector and tensor algebra, theory of invariants
    • Exterior algebra, Grassmann algebras
    • Other algebras built from modules
    • Applications of matrix theory to physics
    • Miscellaneous topics

• Associative rings and algebras

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • General and miscellaneous
    • Category-theoretic methods and results (except as in 16D90)
    • Applications of logic
    • None of the above, but in this section
    • Modules, bimodules and ideals
    • General module theory
    • Bimodules
    • Ideals
    • Infinite-dimensional simple rings (except as in 16Kxx)
    • Free, projective, and flat modules and ideals
    • Injective modules, self-injective rings
    • Simple and semisimple modules, primitive rings and ideals
    • Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
    • Other classes of modules and ideals
    • Module categories; module theory in a category-theoretic context; Morita equivalence and duality
    • None of the above, but in this section
    • Homological methods
    • Syzygies, resolutions, complexes
    • Homological dimension
    • Grothendieck groups, $K$-theory, etc.
    • Homological functors on modules (Tor, Ext, etc.)
    • (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
    • Differential graded algebras and applications
    • von Neumann regular rings and generalizations
    • Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
    • Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
    • None of the above, but in this section
    • Representation theory of rings and algebras
    • Representations of Artinian rings
    • Representations of quivers and partially ordered sets
    • Representations of orders, lattices, algebras over commutative rings
    • Cohen-Macaulay modules
    • Representation type (finite, tame, wild, etc.)
    • Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
    • None of the above, but in this section
    • Orders and arithmetic, separable algebras, Azumaya algebras
    • Division rings and semisimple Artin rings
    • Finite-dimensional
    • Infinite-dimensional and general
    • Brauer groups
    • None of the above, but in this section
    • Local rings and generalizations
    • Noncommutative local and semilocal rings, perfect rings
    • Quasi-Frobenius rings
    • None of the above, but in this section
    • Radicals and radical properties of rings
    • Jacobson radical, quasimultiplication
    • Nil and nilpotent radicals, sets, ideals, rings
    • Prime and semiprime rings
    • General radicals and rings
    • None of the above, but in this section
    • Chain conditions, growth conditions, and other forms of finiteness
    • Finite rings and finite-dimensional algebras
    • Artinian rings and modules
    • Noetherian rings and modules
    • Localization and Noetherian rings
    • Chain conditions on annihilators and summands: Goldie-type conditions, Krull dimension
    • Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
    • Growth rate, Gelfand-Kirillov dimension
    • None of the above, but in this section
    • Rings with polynomial identity
    • $T$-ideals, identities, varieties of rings and algebras
    • Semiprime p.i. rings, rings embeddable in matrices over commutative rings
    • Trace rings and invariant theory
    • Identities other than those of matrices over commutative rings
    • Other kinds of identities (generalized polynomial, rational, involution)
    • None of the above, but in this section
    • Rings and algebras arising under various constructions
    • Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
    • Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
    • Centralizing and normalizing extensions
    • Universal enveloping algebras of Lie algebras
    • Rings of differential operators
    • Group rings, Laurent polynomial rings
    • Twisted and skew group rings, crossed products
    • Ordinary and skew polynomial rings and semigroup rings
    • Quadratic and Koszul algebras
    • Rings arising from non-commutative algebraic geometry
    • Smash products of general Hopf actions
    • Endomorphism rings; matrix rings
    • Rings of functions, subdirect products, sheaves of rings
    • Extensions of rings by ideals
    • Deformations of rings
    • Maximal ring of quotients, torsion theories, radicals on module categories
    • None of the above, but in this section
    • Conditions on elements
    • Integral domains
    • Ore rings, multiplicative sets, Ore localization
    • Divisibility, noncommutative UFDs
    • Units, groups of units
    • Center, normalizer (invariant elements)
    • Generalizations of commutativity
    • None of the above, but in this section
    • Rings and algebras with additional structure
    • Rings with involution; Lie, Jordan and other nonassociative structures
    • Automorphisms and endomorphisms
    • Actions of groups and semigroups; invariant theory
    • Derivations, actions of Lie algebras
    • Coalgebras, bialgebras, Hopf algebras; rings, modules, etc. on which these act
    • Ring-theoretic aspects of quantum groups
    • Graded rings and modules
    • Super'' (or skew’’) structure
    • Valuations, completions, formal power series and related constructions
    • Filtered rings; filtrational and graded techniques
    • Topological and ordered rings and modules
    • None of the above, but in this section
    • Generalizations
    • Near-rings
    • Semirings
    • None of the above, but in this section
    • Computational aspects of associative rings

• Nonassociative rings and algebras

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Computational methods
    • General nonassociative rings
    • General theory
    • Power-associative rings
    • Noncommutative Jordan algebras
    • Flexible algebras
    • Algebras satisfying other identities
    • Leibniz algebras
    • Division algebras
    • Automorphisms, derivations, other operators
    • Ternary compositions
    • Other $n$-ary compositions $(n ge 3)$
    • Quadratic algebras (but not quadratic Jordan algebras)
    • Free algebras
    • Structure theory
    • Radical theory
    • Superalgebras
    • Composition algebras
    • Valued algebras
    • None of the above, but in this section
    • Lie algebras and Lie superalgebras
    • Identities, free Lie (super)algebras
    • Structure theory
    • Representations, algebraic theory (weights)
    • Representations, analytic theory
    • Simple, semisimple, reductive (super)algebras (roots)
    • Exceptional (super)algebras
    • Solvable, nilpotent (super)algebras
    • Universal enveloping (super)algebras
    • Quantum groups (quantized enveloping algebras) and related deformations
    • Automorphisms, derivations, other operators
    • Lie algebras of linear algebraic groups
    • Modular Lie (super)algebras
    • Homological methods in Lie (super)algebras
    • Cohomology of Lie (super)algebras
    • Lie (super)algebras associated with other structures (associative, Jordan, etc.)
    • Lie bialgebras
    • Poisson algebras
    • Infinite-dimensional Lie (super)algebras
    • Lie algebras of vector fields and related (super) algebras
    • Kac-Moody (super)algebras (structure and representation theory)
    • Virasoro and related algebras
    • Vertex operators; vertex operator algebras and related structures
    • Graded Lie (super)algebras
    • Color Lie (super)algebras
    • Applications to integrable systems
    • Applications to physics
    • None of the above, but in this section
    • Jordan algebras (algebras, triples and pairs)
    • Identities and free Jordan structures
    • Structure theory
    • Radicals
    • Simple, semisimple algebras
    • Idempotents, Peirce decompositions
    • Associated groups, automorphisms
    • Associated manifolds
    • Associated geometries
    • Exceptional Jordan structures
    • Jordan structures associated with other structures
    • Finite-dimensional structures
    • Division algebras
    • Jordan structures on Banach spaces and algebras
    • Super structures
    • Applications to physics
    • None of the above, but in this section
    • Other nonassociative rings and algebras
    • Alternative rings
    • Malcev (Maltsev) rings and algebras
    • Right alternative rings
    • $(gamma, delta)$-rings, including $(1,-1)$-rings
    • Lie-admissible algebras
    • Genetic algebras
    • None of the above, but in this section

• Category theory; homological algebra

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • General theory of categories and functors
    • Definitions, generalizations
    • Graphs, diagram schemes, precategories
    • Foundations, relations to logic and deductive systems
    • Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
    • Special properties of functors (faithful, full, etc.)
    • Natural morphisms, dinatural morphisms
    • Functor categories, comma categories
    • Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
    • Factorization of morphisms, substructures, quotient structures, congruences, amalgams
    • Categories admitting limits (complete categories), functors preserving limits, completions
    • Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
    • None of the above, but in this section
    • Special categories
    • Category of sets, characterizations
    • Category of relations, additive relations
    • Embedding theorems, universal categories
    • Categories of machines, automata, operative categories
    • Topoi
    • Categories of topological spaces and continuous mappings
    • Preorders, orders and lattices (viewed as categories)
    • Groupoids, semigroupoids, semigroups, groups (viewed as categories)
    • None of the above, but in this section
    • Categories and theories
    • Equational categories
    • Theories (e.g. algebraic theories), structure, and semantics
    • Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
    • Algebras and Kleisli categories associated with monads
    • Sketches and generalizations
    • Accessible and locally presentable categories
    • Categorical semantics of formal languages
    • None of the above, but in this section
    • Categories with structure
    • Double categories, $2$-categories, bicategories and generalizations
    • Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
    • Closed categories (closed monoidal and Cartesian closed categories, etc.)
    • Enriched categories (over closed or monoidal categories)
    • Strong functors, strong adjunctions
    • Fibered categories
    • Structured objects in a category (group objects, etc.)
    • Operads
    • None of the above, but in this section
    • Abelian categories
    • Preadditive, additive categories
    • Exact categories, abelian categories
    • Grothendieck categories
    • Embedding theorems
    • Derived functors and satellites
    • Derived categories, triangulated categories
    • Localization of categories
    • Torsion theories, radicals
    • None of the above, but in this section
    • Categories and geometry
    • Local categories and functors
    • Grothendieck topologies
    • Abstract manifolds and fiber bundles
    • Presheaves and sheaves
    • Algebraic $K$-theory and $L$-theory
    • Grothendieck groups
    • None of the above, but in this section
    • Homological algebra
    • Projectives and injectives
    • Resolutions; derived functors
    • Ext and Tor, generalizations, Künneth formula
    • Homological dimension
    • Relative homological algebra, projective classes
    • Simplicial sets, simplicial objects (in a category)
    • Chain complexes
    • Spectral sequences, hypercohomology
    • Nonabelian homological algebra
    • Homotopical algebra
    • Other (co)homology theories
    • None of the above, but in this section

• $K$-theory

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Grothendieck groups and $K_0$
    • Stability for projective modules
    • Efficient generation
    • Frobenius induction, Burnside and representation rings
    • $K_0$ of group rings and orders
    • $K_0$ of other rings
    • None of the above, but in this section
    • Whitehead groups and $K_1$
    • Stable range conditions
    • Stability for linear groups
    • $K_1$ of group rings and orders
    • Congruence subgroup problems
    • None of the above, but in this section
    • Steinberg groups and $K_2$
    • Central extensions and Schur multipliers
    • Symbols, presentations and stability of $K_2$
    • $K_2$ and the Brauer group
    • Excision for $K_2$
    • None of the above, but in this section
    • Higher algebraic $K$-theory
    • $Q$- and plus-constructions
    • Algebraic $K$-theory of spaces
    • Symmetric monoidal categories
    • Karoubi-Villamayor-Gersten $K$-theory
    • Negative $K$-theory, NK and Nil
    • Higher symbols, Milnor $K$-theory
    • Computations of higher $K$-theory of rings
    • $K$-theory and homology; cyclic homology and cohomology
    • None of the above, but in this section
    • $K$-theory in geometry
    • $K$-theory of schemes
    • Algebraic cycles and motivic cohomology
    • Relations with cohomology theories
    • None of the above, but in this section
    • $K$-theory in number theory
    • Generalized class field theory
    • Symbols and arithmetic
    • Étale cohomology, higher regulators, zeta and $L$-functions
    • None of the above, but in this section
    • $K$-theory of forms
    • Stability for quadratic modules
    • Witt groups of rings
    • $L$-theory of group rings
    • Hermitian $K$-theory, relations with $K$-theory of rings
    • None of the above, but in this section
    • Obstructions from topology
    • Finiteness and other obstructions in $K_0$
    • Whitehead (and related) torsion
    • Surgery obstructions
    • Obstructions to group actions
    • None of the above, but in this section
    • $K$-theory and operator algebras
    • $K_0$ as an ordered group, traces
    • EXT and $K$-homology
    • Kasparov theory ($KK$-theory)
    • Index theory
    • None of the above, but in this section
    • Topological $K$-theory
    • Riemann-Roch theorems, Chern characters
    • $J$-homomorphism, Adams operations
    • Connective $K$-theory, cobordism
    • Equivariant $K$-theory
    • Computations, geometric applications
    • None of the above, but in this section
    • Miscellaneous applications of $K$-theory

• Group theory and generalizations

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Foundations
    • Axiomatics and elementary properties
    • Metamathematical considerations
    • Applications of logic to group theory
    • None of the above, but in this section
    • Permutation groups
    • General theory for finite groups
    • General theory for infinite groups
    • Characterization theorems
    • Primitive groups
    • Multiply transitive finite groups
    • Multiply transitive infinite groups
    • Finite automorphism groups of algebraic, geometric, or combinatorial structures
    • Infinite automorphism groups
    • Symmetric groups
    • Subgroups of symmetric groups
    • Computational methods
    • None of the above, but in this section
    • Representation theory of groups
    • Group rings of finite groups and their modules
    • Group rings of infinite groups and their modules
    • Hecke algebras and their representations
    • Integral representations of finite groups
    • $p$-adic representations of finite groups
    • Integral representations of infinite groups
    • Ordinary representations and characters
    • Modular representations and characters
    • Projective representations and multipliers
    • Representations of finite symmetric groups
    • Representations of infinite symmetric groups
    • Representations of finite groups of Lie type
    • Representations of sporadic groups
    • Applications of group representations to physics
    • Computational methods
    • None of the above, but in this section
    • Abstract finite groups
    • Classification of simple and nonsolvable groups
    • Simple groups: alternating groups and groups of Lie type
    • Simple groups: sporadic groups
    • Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
    • Nilpotent groups, $p$-groups
    • Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
    • Special subgroups (Frattini, Fitting, etc.)
    • Series and lattices of subgroups
    • Subnormal subgroups
    • Products of subgroups
    • Automorphisms
    • Arithmetic and combinatorial problems
    • None of the above, but in this section
    • Structure and classification of infinite or finite groups
    • Free nonabelian groups
    • Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
    • Subgroup theorems; subgroup growth
    • Groups acting on trees
    • Quasivarieties and varieties of groups
    • Chains and lattices of subgroups, subnormal subgroups
    • Limits, profinite groups
    • Extensions, wreath products, and other compositions
    • Local properties
    • Residual properties and generalizations
    • Maximal subgroups
    • Simple groups
    • General structure theorems
    • General theorems concerning automorphisms of groups
    • Groups with a $BN$-pair; buildings
    • Conjugacy classes
    • None of the above, but in this section
    • Special aspects of infinite or finite groups
    • Generators, relations, and presentations
    • Cancellation theory; application of van Kampen diagrams
    • Word problems, other decision problems, connections with logic and automata
    • Commutator calculus
    • Derived series, central series, and generalizations
    • Solvable groups, supersolvable groups
    • Formations of groups, Fitting classes
    • Nilpotent groups
    • Generalizations of solvable and nilpotent groups
    • Other classes of groups defined by subgroup chains
    • FC-groups and their generalizations
    • Automorphism groups of groups
    • Representations of groups as automorphism groups of algebraic systems
    • Fundamental groups and their automorphisms
    • Braid groups; Artin groups
    • Other groups related to topology or analysis
    • Associated Lie structures
    • Engel conditions
    • Periodic groups; locally finite groups
    • Reflection and Coxeter groups
    • Ordered groups
    • Geometric group theory
    • Hyperbolic groups and nonpositively curved groups
    • Asymptotic properties of groups
    • None of the above, but in this section
    • Linear algebraic groups (classical groups)
    • Representation theory
    • Cohomology theory
    • Linear algebraic groups over arbitrary fields
    • Linear algebraic groups over the reals, the complexes, the quaternions
    • Linear algebraic groups over local fields and their integers
    • Linear algebraic groups over global fields and their integers
    • Linear algebraic groups over adèles and other rings and schemes
    • Linear algebraic groups over finite fields
    • Quantum groups (quantized function algebras) and their representations
    • Applications to physics
    • None of the above, but in this section
    • Other groups of matrices
    • Unimodular groups, congruence subgroups
    • Fuchsian groups and their generalizations
    • Other geometric groups, including crystallographic groups
    • Other matrix groups over fields
    • Other matrix groups over rings
    • Other matrix groups over finite fields
    • None of the above, but in this section
    • Connections with homological algebra and category theory
    • Homological methods in group theory
    • Cohomology of groups
    • Category of groups
    • None of the above, but in this section
    • Abelian groups
    • Finite abelian groups
    • Torsion groups, primary groups and generalized primary groups
    • Torsion-free groups, finite rank
    • Torsion-free groups, infinite rank
    • Mixed groups
    • Direct sums, direct products, etc.
    • Subgroups
    • Automorphisms, homomorphisms, endomorphisms, etc.
    • Extensions
    • Homological and categorical methods
    • Topological methods
    • None of the above, but in this section
    • Groupoids (i.e. small categories in which all morphisms are isomorphisms)
    • Semigroups
    • Free semigroups, generators and relations, word problems
    • Varieties of semigroups
    • General structure theory
    • Radical theory
    • Ideal theory
    • Commutative semigroups
    • Mappings of semigroups
    • Regular semigroups
    • Inverse semigroups
    • Orthodox semigroups
    • Semigroups of transformations, etc.
    • Semigroup rings, multiplicative semigroups of rings
    • Representation of semigroups; actions of semigroups on sets
    • Semigroups in automata theory, linguistics, etc.
    • Connections of semigroups with homological algebra and category theory
    • None of the above, but in this section
    • Other generalizations of groups
    • Sets with a single binary operation (groupoids)
    • Loops, quasigroups
    • Ternary systems (heaps, semiheaps, heapoids, etc.)
    • $n$-ary systems $(nge 3)$
    • Hypergroups
    • Fuzzy groups
    • None of the above, but in this section
    • Probabilistic methods in group theory

• Topological groups, Lie groups

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Topological and differentiable algebraic systems
    • Structure of general topological groups
    • Analysis on general topological groups
    • Structure of topological semigroups
    • Analysis on topological semigroups
    • Topological groupoids (including differentiable and Lie groupoids)
    • Representations of general topological groups and semigroups
    • Topological semilattices, lattices and applications
    • Other topological algebraic systems and their representations
    • None of the above, but in this section
    • Locally compact abelian groups (LCA groups)
    • General properties and structure of LCA groups
    • Structure of group algebras of LCA groups
    • None of the above, but in this section
    • Compact groups
    • Locally compact groups and their algebras
    • General properties and structure of locally compact groups
    • Unitary representations of locally compact groups
    • Other representations of locally compact groups
    • Group algebras of locally compact groups
    • Representations of group algebras
    • $C^$-algebras and $W$-algebras in relation to group representations
    • Induced representations
    • Duality theorems
    • Ergodic theory on groups
    • Automorphism groups of locally compact groups
    • None of the above, but in this section
    • Lie groups
    • Local Lie groups
    • General properties and structure of complex Lie groups
    • General properties and structure of real Lie groups
    • General properties and structure of other Lie groups
    • Nilpotent and solvable Lie groups
    • Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
    • Analysis on real and complex Lie groups
    • Analysis on $p$-adic Lie groups
    • Discrete subgroups of Lie groups
    • Continuous cohomology
    • Structure and representation of the Lorentz group
    • Representations of Lie and linear algebraic groups over real fields: analytic methods
    • Semisimple Lie groups and their representations
    • Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
    • Representations of Lie and linear algebraic groups over local fields
    • Representations of Lie and linear algebraic groups over global fields and adèle rings
    • Lie algebras of Lie groups
    • Infinite-dimensional Lie groups and their Lie algebras
    • Loop groups and related constructions, group-theoretic treatment
    • Applications of Lie groups to physics; explicit representations
    • None of the above, but in this section
    • Noncompact transformation groups
    • General theory of group and pseudogroup actions
    • Measurable group actions
    • Homogeneous spaces
    • Groups as automorphisms of other structures

• Real functions

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Functions of one variable
    • Foundations: limits and generalizations, elementary topology of the line
    • One-variable calculus
    • Elementary functions
    • Rate of growth of functions, orders of infinity, slowly varying functions
    • Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
    • Lipschitz (Hölder) classes
    • Iteration
    • Classification of real functions; Baire classification of sets and functions
    • Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
    • Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
    • Singular functions, Cantor functions, functions with other special properties
    • Fractional derivatives and integrals
    • Antidifferentiation
    • Denjoy and Perron integrals, other special integrals
    • Integrals of Riemann, Stieltjes and Lebesgue type
    • Functions of bounded variation, generalizations
    • Absolutely continuous functions
    • Monotonic functions, generalizations
    • Convexity, generalizations
    • None of the above, but in this section
    • Functions of several variables
    • Continuity and differentiation questions
    • Implicit function theorems, Jacobians, transformations with several variables
    • Calculus of vector functions
    • Integration: length, area, volume
    • Integral formulas (Stokes, Gauss, Green, etc.)
    • Convexity, generalizations
    • Absolutely continuous functions, functions of bounded variation
    • Special properties of functions of several variables, Hölder conditions, etc.
    • Representation and superposition of functions
    • None of the above, but in this section
    • Polynomials, rational functions
    • Polynomials: analytic properties, etc.
    • Polynomials: location of zeros
    • Rational functions
    • None of the above, but in this section
    • Inequalities
    • Inequalities for trigonometric functions and polynomials
    • Inequalities involving other types of functions
    • Inequalities involving derivatives and differential and integral operators
    • Inequalities for sums, series and integrals
    • Other analytical inequalities
    • None of the above, but in this section
    • Miscellaneous topics
    • Real-analytic functions
    • $C^infty$-functions, quasi-analytic functions
    • Calculus of functions on infinite-dimensional spaces
    • Calculus of functions taking values in infinite-dimensional spaces
    • Set-valued functions
    • Non-Archimedean analysis
    • Nonstandard analysis
    • Constructive real analysis
    • Fuzzy real analysis
    • Means
    • None of the above, but in this section

• Measure and integration

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • Classical measure theory
    • Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
    • Real- or complex-valued set functions
    • Contents, measures, outer measures, capacities
    • Abstract differentiation theory, differentiation of set functions
    • Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
    • Integration with respect to measures and other set functions
    • Spaces of measures, convergence of measures
    • Measures and integrals in product spaces
    • Integration and disintegration of measures
    • Lifting theory
    • Measures on Boolean rings, measure algebras
    • Length, area, volume, other geometric measure theory
    • Hausdorff and packing measures
    • Fractals
    • None of the above, but in this section
    • Set functions, measures and integrals with values in abstract spaces
    • Vector-valued set functions, measures and integrals
    • Group- or semigroup-valued set functions, measures and integrals
    • Set functions, measures and integrals with values in ordered spaces
    • Set-valued set functions and measures; integration of set-valued functions; measurable selections
    • None of the above, but in this section
    • Set functions and measures on spaces with additional structure
    • Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
    • Set functions and measures on topological groups, Haar measures, invariant measures
    • Set functions and measures on topological spaces (regularity of measures, etc.)
    • Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
    • None of the above, but in this section
    • Measure-theoretic ergodic theory
    • Measure-preserving transformations
    • One-parameter continuous families of measure-preserving transformations
    • General groups of measure-preserving transformations
    • Entropy and other invariants
    • None of the above, but in this section
    • Miscellaneous topics in measure theory
    • Nonstandard measure theory
    • Fuzzy measure theory
    • Other connections with logic and set theory
    • None of the above, but in this section

• Functions of a complex variable

• • General reference works (handbooks, dictionaries, bibliographies, etc.)
    • Instructional exposition (textbooks, tutorial papers, etc.)
    • Research exposition (monographs, survey articles)
    • Historical (must also be assigned at least one classification number from Section 01)
    • Explicit machine computation and programs (not the theory of computation or programming)
    • Proceedings, conferences, collections, etc.
    • General properties
    • Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
    • Inequalities in the complex domain
    • None of the above, but in this section
    • Series expansions
    • Power series (including lacunary series)
    • Random power series
    • Boundary behavior of power series, over-convergence
    • Analytic continuation
    • Dirichlet series and other series expansions, exponential series
    • Completeness problems, closure of a system of functions
    • Continued fractions
    • None of the above, but in this section
    • Geometric function theory
    • Polynomials
    • Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
    • Conformal mappings of special domains
    • Covering theorems in conformal mapping theory
    • Numerical methods in conformal mapping theory
    • General theory of conformal mappings
    • Kernel functions and applications
    • Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
    • Coefficient problems for univalent and multivalent functions
    • General theory of univalent and multivalent functions
    • Quasiconformal mappings in the plane
    • Quasiconformal mappings in $R^n$, other generalizations
    • Extremal problems for conformal and quasiconformal mappings, variational methods
    • Extremal problems for conformal and quasiconformal mappings, other methods
    • Maximum principle; Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
    • Capacity and harmonic measure in the complex plane
    • None of the above, but in this section
    • Entire and meromorphic functions, and related topics
    • Functional equations in the complex domain, iteration and composition of analytic functions
    • Representations of entire functions by series and integrals
    • Special classes of entire functions and growth estimates
    • Entire functions, general theory
    • Meromorphic functions, general theory
    • Distribution of values, Nevanlinna theory
    • Cluster sets, prime ends, boundary behavior
    • Bloch functions, normal functions, normal families
    • Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
    • [H]^p$-classes](30d55.md “MISSING PAGE”) Quasi-analytic and other classes of functions None of the above, but in this section Miscellaneous topics of analysis in the complex domain Moment problems, interpolation problems Approximation in the complex domain Asymptotic representations in the complex domain Integration, integrals of Cauchy type, integral representations of analytic functions Boundary value problems None of the above, but in this section Riemann surfaces Compact Riemann surfaces and uniformization Harmonic functions on Riemann surfaces Classification theory of Riemann surfaces Ideal boundary theory Differentials on Riemann surfaces Fuchsian groups and automorphic functions Kleinian groups Conformal metrics (hyperbolic, Poincaré, distance functions) Klein surfaces Teichmüller theory None of the above, but in this section Generalized function theory Non-Archimedean function theory; nonstandard function theory Finely holomorphic functions and topological function theory Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.) Discrete analytic functions Other generalizations of analytic functions (including abstract-valued functions) Functions of hypercomplex variables and generalized variables None of the above, but in this section Spaces and algebras of analytic functions

    • Potential theory

    • • General reference works (handbooks, dictionaries, bibliographies, etc.)
        • Instructional exposition (textbooks, tutorial papers, etc.)
        • Research exposition (monographs, survey articles)
        • Historical (must also be assigned at least one classification number from Section 01)
        • Explicit machine computation and programs (not the theory of computation or programming)
        • Proceedings, conferences, collections, etc.
        • Two-dimensional theory
        • Harmonic, subharmonic, superharmonic functions
        • Integral representations, integral operators, integral equations methods
        • Potentials and capacity, harmonic measure, extremal length
        • Boundary behavior (theorems of Fatou type, etc.)
        • Boundary value and inverse problems
        • Biharmonic, polyharmonic functions and equations, Poisson’s equation
        • Connections with differential equations
        • None of the above, but in this section
        • Higher-dimensional theory
        • Harmonic, subharmonic, superharmonic functions
        • Integral representations, integral operators, integral equations methods
        • Potentials and capacities, extremal length
        • Boundary value and inverse problems
        • Boundary behavior
        • Biharmonic and polyharmonic equations and functions
        • Connections with differential equations
        • None of the above, but in this section
        • Other generalizations
        • Harmonic, subharmonic, superharmonic functions
        • Pluriharmonic and plurisubharmonic functions
        • Potential theory on Riemannian manifolds
        • Potentials and capacities
        • Discrete potential theory and numerical methods
        • Dirichlet spaces
        • Martin boundary theory
        • Fine potential theory
        • Other generalizations (nonlinear potential theory, etc.)
        • None of the above, but in this section

    • Axiomatic potential theory

    • • Several complex variables and analytic spaces
        • General reference works (handbooks, dictionaries, bibliographies, etc.)
        • Instructional exposition (textbooks, tutorial papers, etc.)
        • Research exposition (monographs, survey articles)
        • Historical (must also be assigned at least one classification number from Section 01)
        • Explicit machine computation and programs (not the theory of computation or programming)
        • Proceedings, conferences, collections, etc.
        • Holomorphic functions of several complex variables
        • Power series, series of functions
        • Special domains (Reinhardt, Hartogs, circular, tube)
        • Holomorphic functions
        • Multifunctions
        • Entire functions
        • Special families of functions
        • Bloch functions, normal functions
        • Normal families of functions, mappings
        • Meromorphic functions
        • Nevanlinna theory (local); growth estimates; other inequalities
        • Integral representations; canonical kernels (Szegó, Bergman, etc.)
        • Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
        • Local theory of residues
        • Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30)
        • [H]^p$-spaces, Nevanlinna spaces](32a35.md “MISSING PAGE”) Bergman spaces Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) Algebras of holomorphic functions Boundary behavior of holomorphic functions Hyperfunctions Harmonic analysis of several complex variables Singular integrals Zero sets of holomorphic functions Banach algebra techniques Functional analysis techniques None of the above, but in this section Local analytic geometry Analytic algebras and generalizations, preparation theorems Germs of analytic sets, local parametrization Analytic subsets of affine space Semi-analytic sets and subanalytic sets Triangulation and related questions None of the above, but in this section Analytic spaces Real-analytic manifolds, real-analytic spaces Real-analytic sets, complex Nash functions Embedding of real analytic manifolds Complex supergeometry Complex spaces Topology of analytic spaces Normal analytic spaces Embedding of analytic spaces Analytic subsets and submanifolds Integration on analytic sets and spaces, currents Analytic sheaves and cohomology groups Local cohomology of analytic spaces Duality theorems Sheaves of differential operators and their modules, $D$-modules The Levi problem in complex spaces; generalizations Applications to physics None of the above, but in this section Analytic continuation Domains of holomorphy Envelopes of holomorphy Continuation of analytic objects Removable singularities Riemann domains None of the above, but in this section Holomorphic convexity Holomorphically convex complex spaces, reduction theory Stein spaces, Stein manifolds Polynomial convexity Holomorphic and polynomial approximation, Runge pairs, interpolation Global boundary behavior of holomorphic functions The Levi problem None of the above, but in this section Geometric convexity $q$-convexity, $q$-concavity Other notions of convexity Finite-type conditions Topological consequences of geometric convexity Analytical consequences of geometric convexity (vanishing theorems, etc.) Invariant metrics and pseudodistances None of the above, but in this section Deformations of analytic structures Deformations of complex structures Deformations of special (e.g. CR) structures Deformations of fiber bundles Deformations of submanifolds and subspaces Analytic moduli problems Moduli of Riemann surfaces, Teichmüller theory Period matrices, variation of Hodge structure; degenerations Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) Applications to physics None of the above, but in this section Holomorphic mappings and correspondences Holomorphic mappings, (holomorphic) embeddings and related questions Meromorphic mappings Boundary uniqueness of mappings Picard-type theorems and generalizations Value distribution theory in higher dimensions Proper mappings, finiteness theorems Boundary regularity of mappings Iteration problems None of the above, but in this section Compact analytic spaces Compactification of analytic spaces Algebraic dependence theorems Compact surfaces Compact $3$-folds Compact $n$-folds Transcendental methods of algebraic geometry Compact Kähler manifolds: generalizations, classification Applications to physics None of the above, but in this section Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem) Banach analytic spaces Formal and graded complex spaces Differentiable functions on analytic spaces, differentiable spaces None of the above, but in this section Holomorphic fiber spaces Holomorphic bundles and generalizations Sheaves and cohomology of sections of holomorphic vector bundles, general results Bundle convexity Vanishing theorems Twistor theory, double fibrations Applications to physics None of the above, but in this section Complex spaces with a group of automorphisms Complex Lie groups, automorphism groups acting on complex spaces Homogeneous complex manifolds Almost homogeneous manifolds and spaces Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [Automorphism groups of bf C]^n$ and affine manifolds](32m17.md “MISSING PAGE”) Complex vector fields None of the above, but in this section Automorphic functions General theory of automorphic functions of several complex variables Automorphic forms Automorphic functions in symmetric domains None of the above, but in this section Non-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) Complex manifolds Negative curvature manifolds Positive curvature manifolds Kähler manifolds Kähler-Einstein manifolds Calabi-Yau theory Stein manifolds Uniformization Complex manifolds as subdomains of Euclidean space Embedding theorems Hyperbolic and Kobayashi hyperbolic manifolds Topological aspects of complex manifolds Classification theorems Almost complex manifolds Pseudoholomorphic curves None of the above, but in this section Singularities Local singularities Invariants of analytic local rings Equisingularity (topological and analytic) Global theory of singularities; cohomological properties Relations with arrangements of hyperplanes Surface and hypersurface singularities Deformations of singularities; vanishing cycles Mixed Hodge theory of singular varieties Monodromy; relations with differential equations and $D$-modules Modifications; resolution of singularities Topological aspects: Lefschetz theorems, topological classification, invariants Milnor fibration; relations with knot theory Stratifications; constructible sheaves; intersection cohomology Singularities of holomorphic vector fields and foliations Other operations on singularities None of the above, but in this section Pseudoconvex domains Domains of holomorphy Strongly pseudoconvex domains Worm domains Finite type domains Geometric and analytic invariants on weakly pseudoconvex boundaries Exhaustion functions Peak functions None of the above, but in this section Pluripotential theory Plurisubharmonic functions and generalizations Plurisubharmonic exhaustion functions General pluripotential theory Capacity theory and generalizations Lelong numbers Removable sets Pluricomplex Green functions Currents None of the above, but in this section CR manifolds CR structures, CR operators, and generalizations CR functions CR manifolds as boundaries of domains Analysis on CR manifolds Extension of functions and other analytic objects from CR manifolds Embeddings of CR manifolds Finite type conditions on CR manifolds Real submanifolds in complex manifolds None of the above, but in this section Differential operators in several variables $overlinepartial$ and $overlinepartial$-Neumann operators $overlinepartial_b$ and $overlinepartial_b$-Neumann operators Complex Monge-Ampère operators Pseudodifferential operators in several complex variables Heat kernels in several complex variables Other partial differential equations of complex analysis None of the above, but in this section

          Special functions (33-XX deals with the properties of functions as functions)

            - [General reference works (handbooks, dictionaries, bibliographies, etc.)](33-00.md "MISSING PAGE")
            - [Instructional exposition (textbooks, tutorial papers, etc.)](33-01.md "MISSING PAGE")
            - [Research exposition (monographs, survey articles)](33-02.md "MISSING PAGE")
            - [Historical (must also be assigned at least one classification number from Section 01)](33-03.md "MISSING PAGE")
            - [Explicit machine computation and programs (not the theory of computation or programming)](33-04.md "MISSING PAGE")
            - [Proceedings, conferences, collections, etc.](33-06.md "MISSING PAGE")
            - [Elementary classical functions](33bxx.md "MISSING PAGE")
            - [Exponential and trigonometric functions](33b10.md "MISSING PAGE")
            - [Gamma, beta and polygamma functions](33b15.md "MISSING PAGE")
            - [Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)](33b20.md "MISSING PAGE")
            - [Higher logarithm functions](33b30.md "MISSING PAGE")
            - [None of the above, but in this section](33b99.md "MISSING PAGE")
            - [Hypergeometric functions](33cxx.md "MISSING PAGE")
            - [Classical hypergeometric functions, $_2F_1$](33c05.md "MISSING PAGE")
            - [Bessel and Airy functions, cylinder functions, $_0F_1$](33c10.md "MISSING PAGE")
            - [Confluent hypergeometric functions, Whittaker functions, $_1F_1$](33c15.md "MISSING PAGE")
            - [Generalized hypergeometric series, $_pF_q$](33c20.md "MISSING PAGE")
            - [Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)](33c45.md "MISSING PAGE")
            - [Other special orthogonal polynomials and functions](33c47.md "MISSING PAGE")
            - [Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable](33c50.md "MISSING PAGE")
            - [Orthogonal polynomials and functions associated with root systems](33c52.md "MISSING PAGE")
            - [Spherical harmonics](33c55.md "MISSING PAGE")
            - [Hypergeometric integrals and functions defined by them ($E$, $G$ and H]$ functions)](33c60.md "MISSING PAGE")
              [Appell, Horn and Lauricella functions](33c65.md "MISSING PAGE")
              [Hypergeometric functions associated with root systems](33c67.md "MISSING PAGE")
              [Other hypergeometric functions and integrals in several variables](33c70.md "MISSING PAGE")
              [Elliptic integrals as hypergeometric functions](33c75.md "MISSING PAGE")
              [Connections with groups and algebras, and related topics](33c80.md "MISSING PAGE")
              [Applications](33c90.md "MISSING PAGE")
              [None of the above, but in this section](33c99.md "MISSING PAGE")
              [Basic hypergeometric functions](33dxx.md "MISSING PAGE")
              [$q$-gamma functions, $q$-beta functions and integrals](33d05.md "MISSING PAGE")
              [Basic hypergeometric functions in one variable, ]_rphi_s$](33d15.md "MISSING PAGE")
              [Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)](33d45.md "MISSING PAGE")
              [Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable](33d50.md "MISSING PAGE")
              [Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)](33d52.md "MISSING PAGE")
              [Basic hypergeometric integrals and functions defined by them](33d60.md "MISSING PAGE")
              [Bibasic functions and multiple bases](33d65.md "MISSING PAGE")
              [Basic hypergeometric functions associated with root systems](33d67.md "MISSING PAGE")
              [Other basic hypergeometric functions and integrals in several variables](33d70.md "MISSING PAGE")
              [Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics](33d80.md "MISSING PAGE")
              [Applications](33d90.md "MISSING PAGE")
              [None of the above, but in this section](33d99.md "MISSING PAGE")
              [Other special functions](33exx.md "MISSING PAGE")
              [Elliptic functions and integrals](33e05.md "MISSING PAGE")
              [Lamé, Mathieu, and spheroidal wave functions](33e10.md "MISSING PAGE")
              [Mittag-Leffler functions and generalizations](33e12.md "MISSING PAGE")
              [Other wave functions](33e15.md "MISSING PAGE")
              [Painlevé-type functions](33e17.md "MISSING PAGE")
              [Other functions defined by series and integrals](33e20.md "MISSING PAGE")
              [Other functions coming from differential, difference and integral equations](33e30.md "MISSING PAGE")
              [Special functions in characteristic $p$ (gamma functions, etc.)](33e50.md "MISSING PAGE")
              [None of the above, but in this section](33e99.md "MISSING PAGE")
              [Computational aspects](33fxx.md "MISSING PAGE")
              [Numerical approximation](33f05.md "MISSING PAGE")
              [Symbolic computation (Gosper and Zeilberger algorithms, etc.)](33f10.md "MISSING PAGE")
              [None of the above, but in this section](33f99.md "MISSING PAGE")
              [Ordinary differential equations](34-xx.md "MISSING PAGE")
              [General reference works (handbooks, dictionaries, bibliographies, etc.)](34-00.md "MISSING PAGE")
              [Instructional exposition (textbooks, tutorial papers, etc.)](34-01.md "MISSING PAGE")
              [Research exposition (monographs, survey articles)](34-02.md "MISSING PAGE")
              [Historical (must also be assigned at least one classification number from Section 01)](34-03.md "MISSING PAGE")
              [Explicit machine computation and programs (not the theory of computation or programming)](34-04.md "MISSING PAGE")
              [Proceedings, conferences, collections, etc.](34-06.md "MISSING PAGE")
              [General theory](34axx.md "MISSING PAGE")
              [Explicit solutions and reductions](34a05.md "MISSING PAGE")
              [Implicit equations, differential-algebraic equations](34a09.md "MISSING PAGE")
              [Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions](34a12.md "MISSING PAGE")
              [Analytical theory: series, transformations, transforms, operational calculus, etc.](34a25.md "MISSING PAGE")
              [Geometric methods in differential equations](34a26.md "MISSING PAGE")
              [Linear equations and systems, general](34a30.md "MISSING PAGE")
              [Nonlinear equations and systems, general](34a34.md "MISSING PAGE")
              [Differential equations of infinite order](34a35.md "MISSING PAGE")
              [Discontinuous equations](34a36.md "MISSING PAGE")
              [Differential equations with impulses](34a37.md "MISSING PAGE")
              [Differential inequalities](34a40.md "MISSING PAGE")
              [Theoretical approximation of solutions](34a45.md "MISSING PAGE")
              [Inverse problems](34a55.md "MISSING PAGE")
              [Differential inclusions](34a60.md "MISSING PAGE")
              [None of the above, but in this section](34a99.md "MISSING PAGE")
              [Boundary value problems](34bxx.md "MISSING PAGE")
              [Linear boundary value problems](34b05.md "MISSING PAGE")
              [Linear boundary value problems with nonlinear dependence on the spectral parameter](34b07.md "MISSING PAGE")
              [Multi-parameter boundary value problems](34b08.md "MISSING PAGE")
              [Boundary value problems with an indefinite weight](34b09.md "MISSING PAGE")
              [Multipoint boundary value problems](34b10.md "MISSING PAGE")
              [Nonlinear boundary value problems](34b15.md "MISSING PAGE")
              [Singular nonlinear boundary value problems](34b16.md "MISSING PAGE")
              [Positive solutions of nonlinear boundary value problems](34b18.md "MISSING PAGE")
              [Weyl theory and its generalizations](34b20.md "MISSING PAGE")
              [Sturm-Liouville theory](34b24.md "MISSING PAGE")
              [Green functions](34b27.md "MISSING PAGE")
              [Special equations (Mathieu, Hill, Bessel, etc.)](34b30.md "MISSING PAGE")
              [Boundary value problems with impulses](34b37.md "MISSING PAGE")
              [Boundary value problems on infinite intervals](34b40.md "MISSING PAGE")
              [Boundary value problems on graphs and networks](34b45.md "MISSING PAGE")
              [Applications](34b60.md "MISSING PAGE")
              [None of the above, but in this section](34b99.md "MISSING PAGE")
              [Qualitative theory](34cxx.md "MISSING PAGE")
              [Location of integral curves, singular points, limit cycles](34c05.md "MISSING PAGE")
              [Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)](34c07.md "MISSING PAGE")
              [Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)](34c08.md "MISSING PAGE")
              [Oscillation theory, zeros, disconjugacy and comparison theory](34c10.md "MISSING PAGE")
              [Growth, boundedness, comparison of solutions](34c11.md "MISSING PAGE")
              [Monotone systems](34c12.md "MISSING PAGE")
              [Symmetries, invariants](34c14.md "MISSING PAGE")
              [Nonlinear oscillations, coupled oscillators](34c15.md "MISSING PAGE")
              [Transformation and reduction of equations and systems, normal forms](34c20.md "MISSING PAGE")
              [Bifurcation](34c23.md "MISSING PAGE")
              [Periodic solutions](34c25.md "MISSING PAGE")
              [Relaxation oscillations](34c26.md "MISSING PAGE")
              [Almost periodic solutions](34c27.md "MISSING PAGE")
              [Complex behavior, chaotic systems](34c28.md "MISSING PAGE")
              [Averaging method](34c29.md "MISSING PAGE")
              [Manifolds of solutions](34c30.md "MISSING PAGE")
              [Homoclinic and heteroclinic solutions](34c37.md "MISSING PAGE")
              [Equations and systems on manifolds](34c40.md "MISSING PAGE")
              [Equivalence, asymptotic equivalence](34c41.md "MISSING PAGE")
              [Method of integral manifolds](34c45.md "MISSING PAGE")
              [Hysteresis](34c55.md "MISSING PAGE")
              [Applications](34c60.md "MISSING PAGE")
              [None of the above, but in this section](34c99.md "MISSING PAGE")
              [Stability theory](34dxx.md "MISSING PAGE")
              [Asymptotic properties](34d05.md "MISSING PAGE")
              [Characteristic and Lyapunov exponents](34d08.md "MISSING PAGE")
              [Dichotomy, trichotomy](34d09.md "MISSING PAGE")
              [Perturbations](34d10.md "MISSING PAGE")
              [Singular perturbations](34d15.md "MISSING PAGE")
              [Lyapunov stability](34d20.md "MISSING PAGE")
              [Global stability](34d23.md "MISSING PAGE")
              [Structural stability and analogous concepts](34d30.md "MISSING PAGE")
              [Stability of manifolds of solutions](34d35.md "MISSING PAGE")
              [Ultimate boundedness](34d40.md "MISSING PAGE")
              [Attractors](34d45.md "MISSING PAGE")
              [None of the above, but in this section](34d99.md "MISSING PAGE")
              [Asymptotic theory](34exx.md "MISSING PAGE")
              [Asymptotic expansions](34e05.md "MISSING PAGE")
              [Perturbations, asymptotics](34e10.md "MISSING PAGE")
              [Multiple scale methods](34e13.md "MISSING PAGE")
              [Singular perturbations, general theory](34e15.md "MISSING PAGE")
              [Methods of nonstandard analysis](34e18.md "MISSING PAGE")
              [Singular perturbations, turning point theory, WKB methods](34e20.md "MISSING PAGE")
              [None of the above, but in this section](34e99.md "MISSING PAGE")
              [Equations and systems with randomness](34f05.md "MISSING PAGE")
              [Differential equations in abstract spaces](34gxx.md "MISSING PAGE")
              [Linear equations](34g10.md "MISSING PAGE")
              [Nonlinear equations](34g20.md "MISSING PAGE")
              [Evolution inclusions](34g25.md "MISSING PAGE")
              [None of the above, but in this section](34g99.md "MISSING PAGE")
              [Control problems](34h05.md "MISSING PAGE")
              [Functional-differential and differential-difference equations](34kxx.md "MISSING PAGE")
              [General theory](34k05.md "MISSING PAGE")
              [Linear functional-differential equations](34k06.md "MISSING PAGE")
              [Theoretical approximation of solutions](34k07.md "MISSING PAGE")
              [Boundary value problems](34k10.md "MISSING PAGE")
              [Oscillation theory](34k11.md "MISSING PAGE")
              [Growth, boundedness, comparison of solutions](34k12.md "MISSING PAGE")
              [Periodic solutions](34k13.md "MISSING PAGE")
              [Almost periodic solutions](34k14.md "MISSING PAGE")
              [Transformation and reduction of equations and systems, normal forms](34k17.md "MISSING PAGE")
              [Bifurcation theory](34k18.md "MISSING PAGE")
              [Invariant manifolds](34k19.md "MISSING PAGE")
              [Stability theory](34k20.md "MISSING PAGE")
              [Complex (chaotic) behavior of solutions](34k23.md "MISSING PAGE")
              [Asymptotic theory](34k25.md "MISSING PAGE")
              [Singular perturbations](34k26.md "MISSING PAGE")
              [Numerical approximation of solutions](34k28.md "MISSING PAGE")
              [Inverse problems](34k29.md "MISSING PAGE")
              [Equations in abstract spaces](34k30.md "MISSING PAGE")
              [Control problems](34k35.md "MISSING PAGE")
              [Neutral equations](34k40.md "MISSING PAGE")
              [Equations with impulses](34k45.md "MISSING PAGE")
              [Stochastic delay equations](34k50.md "MISSING PAGE")
              [Applications](34k60.md "MISSING PAGE")
              [None of the above, but in this section](34k99.md "MISSING PAGE")
              [Ordinary differential operators](34lxx.md "MISSING PAGE")
              [General spectral theory](34l05.md "MISSING PAGE")
              [Eigenfunction expansions, completeness of eigenfunctions](34l10.md "MISSING PAGE")
              [Estimation of eigenvalues, upper and lower bounds](34l15.md "MISSING PAGE")
              [Numerical approximation of eigenvalues and of other parts of the spectrum](34l16.md "MISSING PAGE")
              [Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions](34l20.md "MISSING PAGE")
              [Scattering theory](34l25.md "MISSING PAGE")
              [Nonlinear ordinary differential operators](34l30.md "MISSING PAGE")
              [Particular operators (Dirac, one-dimensional Schrödinger, etc.)](34l40.md "MISSING PAGE")
              [None of the above, but in this section](34l99.md "MISSING PAGE")
              [Differential equations in the complex domain](34mxx.md "MISSING PAGE")
              [Entire and meromorphic solutions](34m05.md "MISSING PAGE")
              [Oscillation, growth of solutions](34m10.md "MISSING PAGE")
              [Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)](34m15.md "MISSING PAGE")
              [Nonanalytic aspects](34m20.md "MISSING PAGE")
              [Formal solutions, transform techniques](34m25.md "MISSING PAGE")
              [Asymptotics, summation methods](34m30.md "MISSING PAGE")
              [Singularities, monodromy, local behavior of solutions, normal forms](34m35.md "MISSING PAGE")
              [Resurgence phenomena](34m37.md "MISSING PAGE")
              [Stokes phenomena and connection problems (linear and nonlinear)](34m40.md "MISSING PAGE")
              [Differential equations on complex manifolds](34m45.md "MISSING PAGE")
              [Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)](34m50.md "MISSING PAGE")
              [Painlevé and other special equations; classification, hierarchies; isomonodromic deformations](34m55.md "MISSING PAGE")
              [Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent)](34m60.md "MISSING PAGE")
              [None of the above, but in this section](34m99.md "MISSING PAGE")
              ## [Partial differential equations](35-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](35-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](35-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](35-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](35-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](35-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](35-06.md "MISSING PAGE")
                      - [General theory](35axx.md "MISSING PAGE")
                      - [General existence and uniqueness theorems](35a05.md "MISSING PAGE")
                      - [Local existence and uniqueness theorems](35a07.md "MISSING PAGE")
                      - [Fundamental solutions](35a08.md "MISSING PAGE")
                      - [Cauchy-Kovalevskaya theorems](35a10.md "MISSING PAGE")
                      - [Variational methods](35a15.md "MISSING PAGE")
                      - [Parametrices](35a17.md "MISSING PAGE")
                      - [Wave front sets](35a18.md "MISSING PAGE")
                      - [Analytic methods, singularities](35a20.md "MISSING PAGE")
                      - [Propagation of singularities](35a21.md "MISSING PAGE")
                      - [Transform methods (e.g. integral transforms)](35a22.md "MISSING PAGE")
                      - [Other special methods](35a25.md "MISSING PAGE")
                      - [Microlocal methods; methods of sheaf theory and homological algebra in PDE](35a27.md "MISSING PAGE")
                      - [Geometric theory, characteristics, transformations](35a30.md "MISSING PAGE")
                      - [Theoretical approximation to solutions](35a35.md "MISSING PAGE")
                      - [None of the above, but in this section](35a99.md "MISSING PAGE")
                      - [Qualitative properties of solutions](35bxx.md "MISSING PAGE")
                      - [General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)](35b05.md "MISSING PAGE")
                      - [Periodic solutions](35b10.md "MISSING PAGE")
                      - [Almost periodic solutions](35b15.md "MISSING PAGE")
                      - [Perturbations](35b20.md "MISSING PAGE")
                      - [Singular perturbations](35b25.md "MISSING PAGE")
                      - [Homogenization; partial differential equations in media with periodic structure](35b27.md "MISSING PAGE")
                      - [Dependence of solutions of PDE on initial and boundary data, parameters](35b30.md "MISSING PAGE")
                      - [Bifurcation](35b32.md "MISSING PAGE")
                      - [Critical exponents](35b33.md "MISSING PAGE")
                      - [Resonances](35b34.md "MISSING PAGE")
                      - [Stability, boundedness](35b35.md "MISSING PAGE")
                      - [PDE in connection with control problems](35b37.md "MISSING PAGE")
                      - [Critical points](35b38.md "MISSING PAGE")
                      - [Asymptotic behavior of solutions](35b40.md "MISSING PAGE")
                      - [Attractors](35b41.md "MISSING PAGE")
                      - [Inertial manifolds](35b42.md "MISSING PAGE")
                      - [A priori estimates](35b45.md "MISSING PAGE")
                      - [Maximum principles](35b50.md "MISSING PAGE")
                      - [Continuation and prolongation of solutions of PDE](35b60.md "MISSING PAGE")
                      - [Smoothness and regularity of solutions of PDE](35b65.md "MISSING PAGE")
                      - [None of the above, but in this section](35b99.md "MISSING PAGE")
                      - [Representations of solutions](35cxx.md "MISSING PAGE")
                      - [Solutions in closed form](35c05.md "MISSING PAGE")
                      - [Series solutions, expansion theorems](35c10.md "MISSING PAGE")
                      - [Integral representations of solutions of PDE](35c15.md "MISSING PAGE")
                      - [Asymptotic expansions](35c20.md "MISSING PAGE")
                      - [None of the above, but in this section](35c99.md "MISSING PAGE")
                      - [Generalized solutions of partial differential equations](35dxx.md "MISSING PAGE")
                      - [Existence of generalized solutions](35d05.md "MISSING PAGE")
                      - [Regularity of generalized solutions](35d10.md "MISSING PAGE")
                      - [None of the above, but in this section](35d99.md "MISSING PAGE")
                      - [Equations and systems with constant coefficients](35exx.md "MISSING PAGE")
                      - [Fundamental solutions](35e05.md "MISSING PAGE")
                      - [Convexity properties](35e10.md "MISSING PAGE")
                      - [Initial value problems](35e15.md "MISSING PAGE")
                      - [General theory](35e20.md "MISSING PAGE")
                      - [None of the above, but in this section](35e99.md "MISSING PAGE")
                      - [General first-order equations and systems](35fxx.md "MISSING PAGE")
                      - [General theory of linear first-order PDE](35f05.md "MISSING PAGE")
                      - [Initial value problems for linear first-order PDE, linear evolution equations](35f10.md "MISSING PAGE")
                      - [Boundary value problems for linear first-order PDE](35f15.md "MISSING PAGE")
                      - [General theory of nonlinear first-order PDE](35f20.md "MISSING PAGE")
                      - [Initial value problems for nonlinear first-order PDE, nonlinear evolution equations](35f25.md "MISSING PAGE")
                      - [Boundary value problems for nonlinear first-order PDE](35f30.md "MISSING PAGE")
                      - [None of the above, but in this section](35f99.md "MISSING PAGE")
                      - [General higher-order equations and systems](35gxx.md "MISSING PAGE")
                      - [General theory of linear higher-order PDE](35g05.md "MISSING PAGE")
                      - [Initial value problems for linear higher-order PDE, linear evolution equations](35g10.md "MISSING PAGE")
                      - [Boundary value problems for linear higher-order PDE](35g15.md "MISSING PAGE")
                      - [General theory of nonlinear higher-order PDE](35g20.md "MISSING PAGE")
                      - [Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations](35g25.md "MISSING PAGE")
                      - [Boundary value problems for nonlinear higher-order PDE](35g30.md "MISSING PAGE")
                      - [None of the above, but in this section](35g99.md "MISSING PAGE")
                      - [Close-to-elliptic equations](35hxx.md "MISSING PAGE")
                      - [Hypoelliptic equations](35h10.md "MISSING PAGE")
                      - [Subelliptic equations](35h20.md "MISSING PAGE")
                      - [Quasi-elliptic equations](35h30.md "MISSING PAGE")
                      - [None of the above, but in this section](35h99.md "MISSING PAGE")
                      - [Partial differential equations of elliptic type](35jxx.md "MISSING PAGE")
                      - [Laplace equation, reduced wave equation (Helmholtz), Poisson equation](35j05.md "MISSING PAGE")
                      - [Schrödinger operator](35j10.md "MISSING PAGE")
                      - [General theory of second-order, elliptic equations](35j15.md "MISSING PAGE")
                      - [Variational methods for second-order, elliptic equations](35j20.md "MISSING PAGE")
                      - [Boundary value problems for second-order, elliptic equations](35j25.md "MISSING PAGE")
                      - [General theory of higher-order, elliptic equations](35j30.md "MISSING PAGE")
                      - [Variational methods for higher-order, elliptic equations](35j35.md "MISSING PAGE")
                      - [Boundary value problems for higher-order, elliptic equations](35j40.md "MISSING PAGE")
                      - [General theory of elliptic systems of PDE](35j45.md "MISSING PAGE")
                      - [Variational methods for elliptic systems](35j50.md "MISSING PAGE")
                      - [Boundary value problems for elliptic systems](35j55.md "MISSING PAGE")
                      - [Nonlinear PDE of elliptic type](35j60.md "MISSING PAGE")
                      - [Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE](35j65.md "MISSING PAGE")
                      - [Boundary values of solutions to elliptic PDE](35j67.md "MISSING PAGE")
                      - [Elliptic partial differential equations of degenerate type](35j70.md "MISSING PAGE")
                      - [Unilateral problems and variational inequalities for elliptic PDE](35j85.md "MISSING PAGE")
                      - [None of the above, but in this section](35j99.md "MISSING PAGE")
                      - [Parabolic equations and systems](35kxx.md "MISSING PAGE")
                      - [Heat equation](35k05.md "MISSING PAGE")
                      - [General theory of second-order, parabolic equations](35k10.md "MISSING PAGE")
                      - [Initial value problems for second-order, parabolic equations](35k15.md "MISSING PAGE")
                      - [Boundary value problems for second-order, parabolic equations](35k20.md "MISSING PAGE")
                      - [General theory of higher-order, parabolic equations](35k25.md "MISSING PAGE")
                      - [Initial value problems for higher-order, parabolic equations](35k30.md "MISSING PAGE")
                      - [Boundary value problems for higher-order, parabolic equations](35k35.md "MISSING PAGE")
                      - [General theory of parabolic systems of PDE](35k40.md "MISSING PAGE")
                      - [Initial value problems for parabolic systems](35k45.md "MISSING PAGE")
                      - [Boundary value problems for parabolic systems](35k50.md "MISSING PAGE")
                      - [Nonlinear PDE of parabolic type](35k55.md "MISSING PAGE")
                      - [Reaction-diffusion equations](35k57.md "MISSING PAGE")
                      - [Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE](35k60.md "MISSING PAGE")
                      - [Parabolic partial differential equations of degenerate type](35k65.md "MISSING PAGE")
                      - [Ultraparabolic, pseudoparabolic PDE, etc.](35k70.md "MISSING PAGE")
                      - [Unilateral problems and variational inequalities for parabolic PDE](35k85.md "MISSING PAGE")
                      - [Abstract parabolic evolution equations](35k90.md "MISSING PAGE")
                      - [None of the above, but in this section](35k99.md "MISSING PAGE")
                      - [Partial differential equations of hyperbolic type](35lxx.md "MISSING PAGE")
                      - [Wave equation](35l05.md "MISSING PAGE")
                      - [General theory of second-order, hyperbolic equations](35l10.md "MISSING PAGE")
                      - [Initial value problems for second-order, hyperbolic equations](35l15.md "MISSING PAGE")
                      - [Boundary value problems for second-order, hyperbolic equations](35l20.md "MISSING PAGE")
                      - [General theory of higher-order, hyperbolic equations](35l25.md "MISSING PAGE")
                      - [Initial value problems for higher-order, hyperbolic equations](35l30.md "MISSING PAGE")
                      - [Boundary value problems for higher-order, hyperbolic equations](35l35.md "MISSING PAGE")
                      - [General theory of hyperbolic systems of first-order PDE](35l40.md "MISSING PAGE")
                      - [Initial value problems for hyperbolic systems of first-order PDE](35l45.md "MISSING PAGE")
                      - [Boundary value problems for hyperbolic systems of first-order PDE](35l50.md "MISSING PAGE")
                      - [Hyperbolic systems of higher-order PDE](35l55.md "MISSING PAGE")
                      - [Nonlinear first-order PDE of hyperbolic type](35l60.md "MISSING PAGE")
                      - [Conservation laws](35l65.md "MISSING PAGE")
                      - [Shocks and singularities](35l67.md "MISSING PAGE")
                      - [Nonlinear second-order PDE of hyperbolic type](35l70.md "MISSING PAGE")
                      - [Nonlinear hyperbolic PDE of higher ($gtr 2$) order](35l75.md "MISSING PAGE")
                      - [Hyperbolic PDE of degenerate type](35l80.md "MISSING PAGE")
                      - [Pseudohyperbolic equations](35l82.md "MISSING PAGE")
                      - [Unilateral problems; variational inequalities for hyperbolic PDE](35l85.md "MISSING PAGE")
                      - [Abstract hyperbolic evolution equations](35l90.md "MISSING PAGE")
                      - [None of the above, but in this section](35l99.md "MISSING PAGE")
                      - [Partial differential equations of special type (mixed, composite, etc.)](35mxx.md "MISSING PAGE")
                      - [PDE of mixed type](35m10.md "MISSING PAGE")
                      - [PDE of composite type](35m20.md "MISSING PAGE")
                      - [None of the above, but in this section](35m99.md "MISSING PAGE")
                      - [Overdetermined systems](35nxx.md "MISSING PAGE")
                      - [Overdetermined systems with constant coefficients](35n05.md "MISSING PAGE")
                      - [Overdetermined systems with variable coefficients (general)](35n10.md "MISSING PAGE")
                      - [$overlinepartial$-Neumann problem and generalizations; formal complexes](35n15.md "MISSING PAGE")
                      - [None of the above, but in this section](35n99.md "MISSING PAGE")
                      - [Spectral theory and eigenvalue problems for partial differential operators](35pxx.md "MISSING PAGE")
                      - [General spectral theory of PDE](35p05.md "MISSING PAGE")
                      - [Completeness of eigenfunctions, eigenfunction expansions for PDO](35p10.md "MISSING PAGE")
                      - [Estimation of eigenvalues, upper and lower bounds](35p15.md "MISSING PAGE")
                      - [Asymptotic distribution of eigenvalues and eigenfunctions for PDO](35p20.md "MISSING PAGE")
                      - [Scattering theory for PDE](35p25.md "MISSING PAGE")
                      - [Nonlinear eigenvalue problems, nonlinear spectral theory for PDO](35p30.md "MISSING PAGE")
                      - [None of the above, but in this section](35p99.md "MISSING PAGE")
                      - [Equations of mathematical physics and other areas of application](35qxx.md "MISSING PAGE")
                      - [Euler-Poisson-Darboux equation and generalizations](35q05.md "MISSING PAGE")
                      - [Riemann-Hilbert problems](35q15.md "MISSING PAGE")
                      - [Stokes and Navier-Stokes equations](35q30.md "MISSING PAGE")
                      - [Other equations arising in fluid mechanics](35q35.md "MISSING PAGE")
                      - [Equations from quantum mechanics](35q40.md "MISSING PAGE")
                      - [Solitons](35q51.md "MISSING PAGE")
                      - [KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.)](35q53.md "MISSING PAGE")
                      - [NLS-like (nonlinear Schrödinger) equations](35q55.md "MISSING PAGE")
                      - [Other completely integrable equations](35q58.md "MISSING PAGE")
                      - [Equations of electromagnetic theory and optics](35q60.md "MISSING PAGE")
                      - [Other equations from mechanics](35q72.md "MISSING PAGE")
                      - [PDE in relativity](35q75.md "MISSING PAGE")
                      - [Applications of PDE in areas other than physics](35q80.md "MISSING PAGE")
                      - [None of the above, but in this section](35q99.md "MISSING PAGE")
                      - [Miscellaneous topics involving partial differential equations](35rxx.md "MISSING PAGE")
                      - [PDE with discontinuous coefficients or data](35r05.md "MISSING PAGE")
                      - [Partial functional-differential or differential-difference equations, with or without deviating arguments](35r10.md "MISSING PAGE")
                      - [Impulsive partial differential equations](35r12.md "MISSING PAGE")
                      - [Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables)](35r15.md "MISSING PAGE")
                      - [Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions)](35r20.md "MISSING PAGE")
                      - [Improperly posed problems for PDE](35r25.md "MISSING PAGE")
                      - [Inverse problems (undetermined coefficients, etc.) for PDE](35r30.md "MISSING PAGE")
                      - [Free boundary problems for PDE](35r35.md "MISSING PAGE")
                      - [Partial differential inequalities](35r45.md "MISSING PAGE")
                      - [Partial differential equations of infinite order](35r50.md "MISSING PAGE")
                      - [Partial differential equations with randomness](35r60.md "MISSING PAGE")
                      - [PDE with multivalued right-hand sides](35r70.md "MISSING PAGE")
                      - [None of the above, but in this section](35r99.md "MISSING PAGE")
                      - [Pseudodifferential operators and other generalizations of partial differential operators](35sxx.md "MISSING PAGE")
                      - [General theory of PsDO](35s05.md "MISSING PAGE")
                      - [Initial value problems for PsDO](35s10.md "MISSING PAGE")
                      - [Boundary value problems for PsDO](35s15.md "MISSING PAGE")
                      - [Fourier integral operators](35s30.md "MISSING PAGE")
                      - [Topological aspects: intersection cohomology, stratified sets, etc.](35s35.md "MISSING PAGE")
                      - [Paradifferential operators](35s50.md "MISSING PAGE")
                      - [None of the above, but in this section](35s99.md "MISSING PAGE")
              ## [Dynamical systems and ergodic theory](37-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](37-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](37-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](37-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](37-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](37-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](37-06.md "MISSING PAGE")
                      - [Ergodic theory](37axx.md "MISSING PAGE")
                      - [Measure-preserving transformations](37a05.md "MISSING PAGE")
                      - [One-parameter continuous families of measure-preserving transformations](37a10.md "MISSING PAGE")
                      - [General groups of measure-preserving transformations](37a15.md "MISSING PAGE")
                      - [Homogeneous flows](37a17.md "MISSING PAGE")
                      - [Orbit equivalence, cocycles, ergodic equivalence relations](37a20.md "MISSING PAGE")
                      - [Ergodicity, mixing, rates of mixing](37a25.md "MISSING PAGE")
                      - [Ergodic theorems, spectral theory, Markov operators](37a30.md "MISSING PAGE")
                      - [Entropy and other invariants, isomorphism, classification](37a35.md "MISSING PAGE")
                      - [Nonsingular (and infinite-measure preserving) transformations](37a40.md "MISSING PAGE")
                      - [Relations with number theory and harmonic analysis](37a45.md "MISSING PAGE")
                      - [Relations with probability theory and stochastic processes](37a50.md "MISSING PAGE")
                      - [Relations with the theory of $C^*$-algebras](37a55.md "MISSING PAGE")
                      - [Dynamical systems in statistical mechanics](37a60.md "MISSING PAGE")
                      - [None of the above, but in this section](37a99.md "MISSING PAGE")
                      - [Topological dynamics](37bxx.md "MISSING PAGE")
                      - [Transformations and group actions with special properties (minimality, distality, proximality, etc.)](37b05.md "MISSING PAGE")
                      - [Symbolic dynamics](37b10.md "MISSING PAGE")
                      - [Cellular automata](37b15.md "MISSING PAGE")
                      - [Notions of recurrence](37b20.md "MISSING PAGE")
                      - [Lyapunov functions and stability; attractors, repellers](37b25.md "MISSING PAGE")
                      - [Index theory, Morse-Conley indices](37b30.md "MISSING PAGE")
                      - [Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets](37b35.md "MISSING PAGE")
                      - [Topological entropy](37b40.md "MISSING PAGE")
                      - [Continua theory in dynamics](37b45.md "MISSING PAGE")
                      - [Multi-dimensional shifts of finite type, tiling dynamics](37b50.md "MISSING PAGE")
                      - [Nonautonomous dynamical systems](37b55.md "MISSING PAGE")
                      - [None of the above, but in this section](37b99.md "MISSING PAGE")
                      - [Smooth dynamical systems: general theory](37cxx.md "MISSING PAGE")
                      - [Smooth mappings and diffeomorphisms](37c05.md "MISSING PAGE")
                      - [Vector fields, flows, ordinary differential equations](37c10.md "MISSING PAGE")
                      - [Topological and differentiable equivalence, conjugacy, invariants, moduli, classification](37c15.md "MISSING PAGE")
                      - [Generic properties, structural stability](37c20.md "MISSING PAGE")
                      - [Fixed points, periodic points, fixed-point index theory](37c25.md "MISSING PAGE")
                      - [Periodic orbits of vector fields and flows](37c27.md "MISSING PAGE")
                      - [Homoclinic and heteroclinic orbits](37c29.md "MISSING PAGE")
                      - [Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems](37c30.md "MISSING PAGE")
                      - [Orbit growth](37c35.md "MISSING PAGE")
                      - [Smooth ergodic theory, invariant measures](37c40.md "MISSING PAGE")
                      - [Dimension theory of dynamical systems](37c45.md "MISSING PAGE")
                      - [Approximate trajectories (pseudotrajectories, shadowing, etc.)](37c50.md "MISSING PAGE")
                      - [Periodic and quasiperiodic flows and diffeomorphisms](37c55.md "MISSING PAGE")
                      - [Nonautonomous smooth dynamical systems](37c60.md "MISSING PAGE")
                      - [Monotone flows](37c65.md "MISSING PAGE")
                      - [Attractors and repellers, topological structure](37c70.md "MISSING PAGE")
                      - [Stability theory](37c75.md "MISSING PAGE")
                      - [Symmetries, equivariant dynamical systems](37c80.md "MISSING PAGE")
                      - [Dynamics of group actions other than <B>Z</B> and <B>R</B>, and foliations](37c85.md "MISSING PAGE")
                      - [None of the above, but in this section](37c99.md "MISSING PAGE")
                      - [Dynamical systems with hyperbolic behavior](37dxx.md "MISSING PAGE")
                      - [Hyperbolic orbits and sets](37d05.md "MISSING PAGE")
                      - [Invariant manifold theory](37d10.md "MISSING PAGE")
                      - [Morse-Smale systems](37d15.md "MISSING PAGE")
                      - [Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)](37d20.md "MISSING PAGE")
                      - [Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)](37d25.md "MISSING PAGE")
                      - [Partially hyperbolic systems and dominated splittings](37d30.md "MISSING PAGE")
                      - [Thermodynamic formalism, variational principles, equilibrium states](37d35.md "MISSING PAGE")
                      - [Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)](37d40.md "MISSING PAGE")
                      - [Strange attractors, chaotic dynamics](37d45.md "MISSING PAGE")
                      - [Hyperbolic systems with singularities (billiards, etc.)](37d50.md "MISSING PAGE")
                      - [None of the above, but in this section](37d99.md "MISSING PAGE")
                      - [Low-dimensional dynamical systems](37exx.md "MISSING PAGE")
                      - [Maps of the interval (piecewise continuous, continuous, smooth)](37e05.md "MISSING PAGE")
                      - [Maps of the circle](37e10.md "MISSING PAGE")
                      - [Combinatorial dynamics (types of periodic orbits)](37e15.md "MISSING PAGE")
                      - [Universality, renormalization](37e20.md "MISSING PAGE")
                      - [Maps of trees and graphs](37e25.md "MISSING PAGE")
                      - [Homeomorphisms and diffeomorphisms of planes and surfaces](37e30.md "MISSING PAGE")
                      - [Flows on surfaces](37e35.md "MISSING PAGE")
                      - [Twist maps](37e40.md "MISSING PAGE")
                      - [Rotation numbers and vectors](37e45.md "MISSING PAGE")
                      - [None of the above, but in this section](37e99.md "MISSING PAGE")
                      - [Complex dynamical systems](37fxx.md "MISSING PAGE")
                      - [Relations and correspondences](37f05.md "MISSING PAGE")
                      - [Polynomials; rational maps; entire and meromorphic functions](37f10.md "MISSING PAGE")
                      - [Expanding maps; hyperbolicity; structural stability](37f15.md "MISSING PAGE")
                      - [Combinatorics and topology](37f20.md "MISSING PAGE")
                      - [Renormalization](37f25.md "MISSING PAGE")
                      - [Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems](37f30.md "MISSING PAGE")
                      - [Conformal densities and Hausdorff dimension](37f35.md "MISSING PAGE")
                      - [Geometric limits](37f40.md "MISSING PAGE")
                      - [Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations](37f45.md "MISSING PAGE")
                      - [Small divisors, rotation domains and linearization; Fatou and Julia sets](37f50.md "MISSING PAGE")
                      - [Holomorphic foliations and vector fields](37f75.md "MISSING PAGE")
                      - [None of the above, but in this section](37f99.md "MISSING PAGE")
                      - [Local and nonlocal bifurcation theory](37gxx.md "MISSING PAGE")
                      - [Normal forms](37g05.md "MISSING PAGE")
                      - [Bifurcations of singular points](37g10.md "MISSING PAGE")
                      - [Bifurcations of limit cycles and periodic orbits](37g15.md "MISSING PAGE")
                      - [Hyperbolic singular points with homoclinic trajectories](37g20.md "MISSING PAGE")
                      - [Bifurcations connected with nontransversal intersection](37g25.md "MISSING PAGE")
                      - [Infinite nonwandering sets arising in bifurcations](37g30.md "MISSING PAGE")
                      - [Attractors and their bifurcations](37g35.md "MISSING PAGE")
                      - [Symmetries, equivariant bifurcation theory](37g40.md "MISSING PAGE")
                      - [None of the above, but in this section](37g99.md "MISSING PAGE")
                      - [Random dynamical systems](37hxx.md "MISSING PAGE")
                      - [Foundations, general theory of cocycles, algebraic ergodic theory](37h05.md "MISSING PAGE")
                      - [Generation, random and stochastic difference and differential equations](37h10.md "MISSING PAGE")
                      - [Multiplicative ergodic theory, Lyapunov exponents](37h15.md "MISSING PAGE")
                      - [Bifurcation theory](37h20.md "MISSING PAGE")
                      - [None of the above, but in this section](37h99.md "MISSING PAGE")
                      - [Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems](37jxx.md "MISSING PAGE")
                      - [General theory, relations with symplectic geometry and topology](37j05.md "MISSING PAGE")
                      - [Symplectic mappings, fixed points](37j10.md "MISSING PAGE")
                      - [Symmetries, invariants, invariant manifolds, momentum maps, reduction](37j15.md "MISSING PAGE")
                      - [Bifurcation problems](37j20.md "MISSING PAGE")
                      - [Stability problems](37j25.md "MISSING PAGE")
                      - [Obstructions to integrability (nonintegrability criteria)](37j30.md "MISSING PAGE")
                      - [Completely integrable systems, topological structure of phase space, integration methods](37j35.md "MISSING PAGE")
                      - [Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion](37j40.md "MISSING PAGE")
                      - [Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods](37j45.md "MISSING PAGE")
                      - [Action-minimizing orbits and measures](37j50.md "MISSING PAGE")
                      - [Contact systems](37j55.md "MISSING PAGE")
                      - [Nonholonomic dynamical systems](37j60.md "MISSING PAGE")
                      - [None of the above, but in this section](37j99.md "MISSING PAGE")
                      - [Infinite-dimensional Hamiltonian systems](37kxx.md "MISSING PAGE")
                      - [Hamiltonian structures, symmetries, variational principles, conservation laws](37k05.md "MISSING PAGE")
                      - [Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)](37k10.md "MISSING PAGE")
                      - [Integration of completely integrable systems by inverse spectral and scattering methods](37k15.md "MISSING PAGE")
                      - [Relations with algebraic geometry, complex analysis, special functions](37k20.md "MISSING PAGE")
                      - [Relations with differential geometry](37k25.md "MISSING PAGE")
                      - [Relations with infinite-dimensional Lie algebras and other algebraic structures](37k30.md "MISSING PAGE")
                      - [Lie-Bäcklund and other transformations](37k35.md "MISSING PAGE")
                      - [Soliton theory, asymptotic behavior of solutions](37k40.md "MISSING PAGE")
                      - [Stability problems](37k45.md "MISSING PAGE")
                      - [Bifurcation problems](37k50.md "MISSING PAGE")
                      - [Perturbations, KAM for infinite-dimensional systems](37k55.md "MISSING PAGE")
                      - [Lattice dynamics](37k60.md "MISSING PAGE")
                      - [Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics](37k65.md "MISSING PAGE")
                      - [None of the above, but in this section](37k99.md "MISSING PAGE")
                      - [Infinite-dimensional dissipative dynamical systems](37lxx.md "MISSING PAGE")
                      - [General theory, nonlinear semigroups, evolution equations](37l05.md "MISSING PAGE")
                      - [Normal forms, center manifold theory, bifurcation theory](37l10.md "MISSING PAGE")
                      - [Stability problems](37l15.md "MISSING PAGE")
                      - [Symmetries](37l20.md "MISSING PAGE")
                      - [Inertial manifolds and other invariant attracting sets](37l25.md "MISSING PAGE")
                      - [Attractors and their dimensions, Lyapunov exponents](37l30.md "MISSING PAGE")
                      - [Invariant measures](37l40.md "MISSING PAGE")
                      - [Hyperbolicity; Lyapunov functions](37l45.md "MISSING PAGE")
                      - [Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems](37l50.md "MISSING PAGE")
                      - [Infinite-dimensional random dynamical systems; stochastic equations](37l55.md "MISSING PAGE")
                      - [Lattice dynamics](37l60.md "MISSING PAGE")
                      - [Special approximation methods (nonlinear Galerkin, etc.)](37l65.md "MISSING PAGE")
                      - [None of the above, but in this section](37l99.md "MISSING PAGE")
                      - [Approximation methods and numerical treatment of dynamical systems](37mxx.md "MISSING PAGE")
                      - [Simulation](37m05.md "MISSING PAGE")
                      - [Time series analysis](37m10.md "MISSING PAGE")
                      - [Symplectic integrators](37m15.md "MISSING PAGE")
                      - [Computational methods for bifurcation problems](37m20.md "MISSING PAGE")
                      - [Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)](37m25.md "MISSING PAGE")
                      - [None of the above, but in this section](37m99.md "MISSING PAGE")
                      - [Applications](37nxx.md "MISSING PAGE")
                      - [Dynamical systems in classical and celestial mechanics](37n05.md "MISSING PAGE")
                      - [Dynamical systems in fluid mechanics, oceanography and meteorology](37n10.md "MISSING PAGE")
                      - [Dynamical systems in solid mechanics](37n15.md "MISSING PAGE")
                      - [Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)](37n20.md "MISSING PAGE")
                      - [Dynamical systems in biology](37n25.md "MISSING PAGE")
                      - [Dynamical systems in numerical analysis](37n30.md "MISSING PAGE")
                      - [Dynamical systems in control](37n35.md "MISSING PAGE")
                      - [Dynamical systems in optimization and economics](37n40.md "MISSING PAGE")
                      - [None of the above, but in this section](37n99.md "MISSING PAGE")
              ## [Difference and functional equations](39-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](39-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](39-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](39-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](39-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](39-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](39-06.md "MISSING PAGE")
                      - [Difference equations](39axx.md "MISSING PAGE")
                      - [General](39a05.md "MISSING PAGE")
                      - [Difference equations, additive](39a10.md "MISSING PAGE")
                      - [Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc.](39a11.md "MISSING PAGE")
                      - [Discrete version of topics in analysis](39a12.md "MISSING PAGE")
                      - [Difference equations, scaling ($q$-differences)](39a13.md "MISSING PAGE")
                      - [Multiplicative and other generalized difference equations, e.g. of Lyness type](39a20.md "MISSING PAGE")
                      - [Difference operators](39a70.md "MISSING PAGE")
                      - [None of the above, but in this section](39a99.md "MISSING PAGE")
                      - [Functional equations and inequalities](39bxx.md "MISSING PAGE")
                      - [General](39b05.md "MISSING PAGE")
                      - [Iteration theory, iterative and composite equations](39b12.md "MISSING PAGE")
                      - [Equations for real functions](39b22.md "MISSING PAGE")
                      - [Equations for complex functions](39b32.md "MISSING PAGE")
                      - [Matrix and operator equations](39b42.md "MISSING PAGE")
                      - [Equations for functions with more general domains and/or ranges](39b52.md "MISSING PAGE")
                      - [Orthogonal additivity and other conditional equations](39b55.md "MISSING PAGE")
                      - [Functional inequalities, including subadditivity, convexity, etc.](39b62.md "MISSING PAGE")
                      - [Systems of functional equations and inequalities](39b72.md "MISSING PAGE")
                      - [Stability, separation, extension, and related topics](39b82.md "MISSING PAGE")
                      - [None of the above, but in this section](39b99.md "MISSING PAGE")
              ## [Sequences, series, summability](40-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](40-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](40-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](40-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](40-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](40-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](40-06.md "MISSING PAGE")
                      - [Convergence and divergence of infinite limiting processes](40axx.md "MISSING PAGE")
                      - [Convergence and divergence of series and sequences](40a05.md "MISSING PAGE")
                      - [Convergence and divergence of integrals](40a10.md "MISSING PAGE")
                      - [Convergence and divergence of continued fractions](40a15.md "MISSING PAGE")
                      - [Convergence and divergence of infinite products](40a20.md "MISSING PAGE")
                      - [Approximation to limiting values (summation of series, etc.)](40a25.md "MISSING PAGE")
                      - [Convergence and divergence of series and sequences of functions](40a30.md "MISSING PAGE")
                      - [None of the above, but in this section](40a99.md "MISSING PAGE")
                      - [Multiple sequences and series {(should also be assigned at least one other classification number in this section)]](40b05.md "MISSING PAGE")
                      - [General summability methods](40cxx.md "MISSING PAGE")
                      - [Matrix methods](40c05.md "MISSING PAGE")
                      - [Integral methods](40c10.md "MISSING PAGE")
                      - [Function-theoretic methods (including power series methods and semicontinuous methods)](40c15.md "MISSING PAGE")
                      - [None of the above, but in this section](40c99.md "MISSING PAGE")
                      - [Direct theorems on summability](40dxx.md "MISSING PAGE")
                      - [General theorems](40d05.md "MISSING PAGE")
                      - [Structure of summability fields](40d09.md "MISSING PAGE")
                      - [Tauberian constants and oscillation limits](40d10.md "MISSING PAGE")
                      - [Convergence factors and summability factors](40d15.md "MISSING PAGE")
                      - [Summability and bounded fields of methods](40d20.md "MISSING PAGE")
                      - [Inclusion and equivalence theorems](40d25.md "MISSING PAGE")
                      - [None of the above, but in this section](40d99.md "MISSING PAGE")
                      - [Inversion theorems](40exx.md "MISSING PAGE")
                      - [Tauberian theorems, general](40e05.md "MISSING PAGE")
                      - [Growth estimates](40e10.md "MISSING PAGE")
                      - [Lacunary inversion theorems](40e15.md "MISSING PAGE")
                      - [Tauberian constants](40e20.md "MISSING PAGE")
                      - [None of the above, but in this section](40e99.md "MISSING PAGE")
                      - [Absolute and strong summability](40f05.md "MISSING PAGE")
                      - [Special methods of summability](40gxx.md "MISSING PAGE")
                      - [Cesàro, Euler, Nörlund and Hausdorff methods](40g05.md "MISSING PAGE")
                      - [Abel, Borel and power series methods](40g10.md "MISSING PAGE")
                      - [None of the above, but in this section](40g99.md "MISSING PAGE")
                      - [Functional analytic methods in summability](40h05.md "MISSING PAGE")
                      - [Summability in abstract structures](40j05.md "MISSING PAGE")
              ## [Approximations and expansions](41-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](41-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](41-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](41-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](41-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](41-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](41-06.md "MISSING PAGE")
                      - [Interpolation](41a05.md "MISSING PAGE")
                      - [Approximation by polynomials](41a10.md "MISSING PAGE")
                      - [Spline approximation](41a15.md "MISSING PAGE")
                      - [Inequalities in approximation (Bernstein, Jackson, Nikolcprime skiui-type inequalities)](41a17.md "MISSING PAGE")
                      - [Approximation by rational functions](41a20.md "MISSING PAGE")
                      - [Padé approximation](41a21.md "MISSING PAGE")
                      - [Rate of convergence, degree of approximation](41a25.md "MISSING PAGE")
                      - [Inverse theorems](41a27.md "MISSING PAGE")
                      - [Simultaneous approximation](41a28.md "MISSING PAGE")
                      - [Approximation with constraints](41a29.md "MISSING PAGE")
                      - [Approximation by other special function classes](41a30.md "MISSING PAGE")
                      - [Approximation by operators (in particular, by integral operators)](41a35.md "MISSING PAGE")
                      - [Approximation by positive operators](41a36.md "MISSING PAGE")
                      - [Saturation](41a40.md "MISSING PAGE")
                      - [Best constants](41a44.md "MISSING PAGE")
                      - [Approximation by arbitrary linear expressions](41a45.md "MISSING PAGE")
                      - [Approximation by arbitrary nonlinear expressions; widths and entropy](41a46.md "MISSING PAGE")
                      - [Best approximation, Chebyshev systems](41a50.md "MISSING PAGE")
                      - [Uniqueness of best approximation](41a52.md "MISSING PAGE")
                      - [Approximate quadratures](41a55.md "MISSING PAGE")
                      - [Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)](41a58.md "MISSING PAGE")
                      - [Asymptotic approximations, asymptotic expansions (steepest descent, etc.)](41a60.md "MISSING PAGE")
                      - [Multidimensional problems (should also be assigned at least one other classification number in this section)](41a63.md "MISSING PAGE")
                      - [Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)](41a65.md "MISSING PAGE")
                      - [Remainders in approximation formulas](41a80.md "MISSING PAGE")
                      - [Miscellaneous topics](41a99.md "MISSING PAGE")
              ## [Fourier analysis](42-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](42-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](42-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](42-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](42-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](42-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](42-06.md "MISSING PAGE")
                      - [Fourier analysis in one variable](42axx.md "MISSING PAGE")
                      - [Trigonometric polynomials, inequalities, extremal problems](42a05.md "MISSING PAGE")
                      - [Trigonometric approximation](42a10.md "MISSING PAGE")
                      - [Trigonometric interpolation](42a15.md "MISSING PAGE")
                      - [Fourier coefficients, Fourier series of functions with special properties, special Fourier series](42a16.md "MISSING PAGE")
                      - [Convergence and absolute convergence of Fourier and trigonometric series](42a20.md "MISSING PAGE")
                      - [Summability and absolute summability of Fourier and trigonometric series](42a24.md "MISSING PAGE")
                      - [Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)](42a32.md "MISSING PAGE")
                      - [Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type](42a38.md "MISSING PAGE")
                      - [Multipliers](42a45.md "MISSING PAGE")
                      - [Conjugate functions, conjugate series, singular integrals](42a50.md "MISSING PAGE")
                      - [Lacunary series of trigonometric and other functions; Riesz products](42a55.md "MISSING PAGE")
                      - [Probabilistic methods](42a61.md "MISSING PAGE")
                      - [Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization](42a63.md "MISSING PAGE")
                      - [Completeness of sets of functions](42a65.md "MISSING PAGE")
                      - [Trigonometric moment problems](42a70.md "MISSING PAGE")
                      - [Classical almost periodic functions, mean periodic functions](42a75.md "MISSING PAGE")
                      - [Positive definite functions](42a82.md "MISSING PAGE")
                      - [Convolution, factorization](42a85.md "MISSING PAGE")
                      - [None of the above, but in this section](42a99.md "MISSING PAGE")
                      - [Fourier analysis in several variables](42bxx.md "MISSING PAGE")
                      - [Fourier series and coefficients](42b05.md "MISSING PAGE")
                      - [Summability](42b08.md "MISSING PAGE")
                      - [Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type](42b10.md "MISSING PAGE")
                      - [Multipliers](42b15.md "MISSING PAGE")
                      - [Singular integrals (Calderón-Zygmund, etc.)](42b20.md "MISSING PAGE")
                      - [Maximal functions, Littlewood-Paley theory](42b25.md "MISSING PAGE")
                      - [$H^p$-spaces](42b30.md "MISSING PAGE")
                      - [Function spaces arising in harmonic analysis](42b35.md "MISSING PAGE")
                      - [None of the above, but in this section](42b99.md "MISSING PAGE")
                      - [Nontrigonometric Fourier analysis](42cxx.md "MISSING PAGE")
                      - [Orthogonal functions and polynomials, general theory](42c05.md "MISSING PAGE")
                      - [Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)](42c10.md "MISSING PAGE")
                      - [Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions](42c15.md "MISSING PAGE")
                      - [Rearrangements and other transformations of Fourier and other orthogonal series](42c20.md "MISSING PAGE")
                      - [Uniqueness and localization for orthogonal series](42c25.md "MISSING PAGE")
                      - [Completeness of sets of functions](42c30.md "MISSING PAGE")
                      - [Wavelets](42c40.md "MISSING PAGE")
                      - [None of the above, but in this section](42c99.md "MISSING PAGE")
              ## [Abstract harmonic analysis](43-xx.md "MISSING PAGE")
                      - [General reference works (handbooks, dictionaries, bibliographies, etc.)](43-00.md "MISSING PAGE")
                      - [Instructional exposition (textbooks, tutorial papers, etc.)](43-01.md "MISSING PAGE")
                      - [Research exposition (monographs, survey articles)](43-02.md "MISSING PAGE")
                      - [Historical (must also be assigned at least one classification number from Section 01)](43-03.md "MISSING PAGE")
                      - [Explicit machine computation and programs (not the theory of computation or programming)](43-04.md "MISSING PAGE")
                      - [Proceedings, conferences, collections, etc.](43-06.md "MISSING PAGE")
                      - [Measures on groups and semigroups, etc.](43a05.md "MISSING PAGE")
                      - [Means on groups, semigroups, etc.; amenable groups](43a07.md "MISSING PAGE")
                      - [Measure algebras on groups, semigroups, etc.](43a10.md "MISSING PAGE")
                      - [$L^p$-spaces and other function spaces on groups, semigroups, etc.](43a15.md "MISSING PAGE")
                      - [Analysis on ordered groups, H]^p$-theory](43a17.md "MISSING PAGE")
                        [$L^1$-algebras on groups, semigroups, etc.](43a20.md "MISSING PAGE")
                        [Homomorphisms and multipliers of function spaces on groups, semigroups, etc.](43a22.md "MISSING PAGE")
                        [Fourier and Fourier-Stieltjes transforms on locally compact abelian groups](43a25.md "MISSING PAGE")
                        [Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.](43a30.md "MISSING PAGE")
                        [Other transforms and operators of Fourier type](43a32.md "MISSING PAGE")
                        [Positive definite functions on groups, semigroups, etc.](43a35.md "MISSING PAGE")
                        [Character groups and dual objects](43a40.md "MISSING PAGE")
                        [Spectral synthesis on groups, semigroups, etc.](43a45.md "MISSING PAGE")
                        [Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)](43a46.md "MISSING PAGE")
                        [Convergence of Fourier series and of inverse transforms](43a50.md "MISSING PAGE")
                        [Summability methods on groups, semigroups, etc.](43a55.md "MISSING PAGE")
                        [Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions](43a60.md "MISSING PAGE")
                        [Hypergroups](43a62.md "MISSING PAGE")
                        [Representations of groups, semigroups, etc.](43a65.md "MISSING PAGE")
                        [Analysis on specific locally compact abelian groups](43a70.md "MISSING PAGE")
                        [Analysis on specific compact groups](43a75.md "MISSING PAGE")
                        [Analysis on general compact groups](43a77.md "MISSING PAGE")
                        [Analysis on other specific Lie groups](43a80.md "MISSING PAGE")
                        [Analysis on homogeneous spaces](43a85.md "MISSING PAGE")
                        [Spherical functions](43a90.md "MISSING PAGE")
                        [Categorical methods](43a95.md "MISSING PAGE")
                        [Miscellaneous topics](43a99.md "MISSING PAGE")
                      - ## [Integral transforms, operational calculus](44-xx.md "MISSING PAGE")
                      - - [General reference works (handbooks, dictionaries, bibliographies, etc.)](44-00.md "MISSING PAGE")
                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](44-01.md "MISSING PAGE")
                                  - [Research exposition (monographs, survey articles)](44-02.md "MISSING PAGE")
                                  - [Historical (must also be assigned at least one classification number from Section 01)](44-03.md "MISSING PAGE")
                                  - [Explicit machine computation and programs (not the theory of computation or programming)](44-04.md "MISSING PAGE")
                                  - [Proceedings, conferences, collections, etc.](44-06.md "MISSING PAGE")
                                  - [General transforms](44a05.md "MISSING PAGE")
                                  - [Laplace transform](44a10.md "MISSING PAGE")
                                  - [Radon transform](44a12.md "MISSING PAGE")
                                  - [Special transforms (Legendre, Hilbert, etc.)](44a15.md "MISSING PAGE")
                                  - [Transforms of special functions](44a20.md "MISSING PAGE")
                                  - [Multiple transforms](44a30.md "MISSING PAGE")
                                  - [Convolution](44a35.md "MISSING PAGE")
                                  - [Calculus of Mikusi'nski and other operational calculi](44a40.md "MISSING PAGE")
                                  - [Classical operational calculus](44a45.md "MISSING PAGE")
                                  - [Discrete operational calculus](44a55.md "MISSING PAGE")
                                  - [Moment problems](44a60.md "MISSING PAGE")
                                  - [Miscellaneous topics](44a99.md "MISSING PAGE")
                      - ## [Integral equations](45-xx.md "MISSING PAGE")
                      - - [General reference works (handbooks, dictionaries, bibliographies, etc.)](45-00.md "MISSING PAGE")
                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](45-01.md "MISSING PAGE")
                                  - [Research exposition (monographs, survey articles)](45-02.md "MISSING PAGE")
                                  - [Historical (must also be assigned at least one classification number from Section 01)](45-03.md "MISSING PAGE")
                                  - [Explicit machine computation and programs (not the theory of computation or programming)](45-04.md "MISSING PAGE")
                                  - [Proceedings, conferences, collections, etc.](45-06.md "MISSING PAGE")
                                  - [Linear integral equations](45a05.md "MISSING PAGE")
                                  - [Fredholm integral equations](45b05.md "MISSING PAGE")
                                  - [Eigenvalue problems](45c05.md "MISSING PAGE")
                                  - [Volterra integral equations](45d05.md "MISSING PAGE")
                                  - [Singular integral equations](45exx.md "MISSING PAGE")
                                  - [Integral equations with kernels of Cauchy type](45e05.md "MISSING PAGE")
                                  - [Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)](45e10.md "MISSING PAGE")
                                  - [None of the above, but in this section](45e99.md "MISSING PAGE")
                                  - [Systems of linear integral equations](45fxx.md "MISSING PAGE")
                                  - [Systems of nonsingular linear integral equations](45f05.md "MISSING PAGE")
                                  - [Dual, triple, etc., integral and series equations](45f10.md "MISSING PAGE")
                                  - [Systems of singular linear integral equations](45f15.md "MISSING PAGE")
                                  - [None of the above, but in this section](45f99.md "MISSING PAGE")
                                  - [Nonlinear integral equations](45gxx.md "MISSING PAGE")
                                  - [Singular nonlinear integral equations](45g05.md "MISSING PAGE")
                                  - [Other nonlinear integral equations](45g10.md "MISSING PAGE")
                                  - [Systems of nonlinear integral equations](45g15.md "MISSING PAGE")
                                  - [Miscellaneous special kernels](45h05.md "MISSING PAGE")
                                  - [Integro-ordinary differential equations](45j05.md "MISSING PAGE")
                                  - [Integro-partial differential equations](45k05.md "MISSING PAGE")
                                  - [Theoretical approximation of solutions](45l05.md "MISSING PAGE")
                                  - [Qualitative behavior](45mxx.md "MISSING PAGE")
                                  - [Asymptotics](45m05.md "MISSING PAGE")
                                  - [Stability theory](45m10.md "MISSING PAGE")
                                  - [Periodic solutions](45m15.md "MISSING PAGE")
                                  - [Positive solutions](45m20.md "MISSING PAGE")
                                  - [None of the above, but in this section](45m99.md "MISSING PAGE")
                                  - [Abstract integral equations, integral equations in abstract spaces](45n05.md "MISSING PAGE")
                                  - [Integral operators](45p05.md "MISSING PAGE")
                                  - [Inverse problems](45q05.md "MISSING PAGE")
                                  - [Random integral equations](45r05.md "MISSING PAGE")
                      - ## [Functional analysis](46-xx.md "MISSING PAGE")
                      - - [General reference works (handbooks, dictionaries, bibliographies, etc.)](46-00.md "MISSING PAGE")
                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](46-01.md "MISSING PAGE")
                                  - [Research exposition (monographs, survey articles)](46-02.md "MISSING PAGE")
                                  - [Historical (must also be assigned at least one classification number from Section 01)](46-03.md "MISSING PAGE")
                                  - [Explicit machine computation and programs (not the theory of computation or programming)](46-04.md "MISSING PAGE")
                                  - [Proceedings, conferences, collections, etc.](46-06.md "MISSING PAGE")
                                  - [Topological linear spaces and related structures](46axx.md "MISSING PAGE")
                                  - [General theory of locally convex spaces](46a03.md "MISSING PAGE")
                                  - [Locally convex Fréchet spaces and (DF)-spaces](46a04.md "MISSING PAGE")
                                  - [Barrelled spaces, bornological spaces](46a08.md "MISSING PAGE")
                                  - [Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)](46a11.md "MISSING PAGE")
                                  - [Spaces defined by inductive or projective limits (LB, LF, etc.)](46a13.md "MISSING PAGE")
                                  - [Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)](46a16.md "MISSING PAGE")
                                  - [Bornologies and related structures; Mackey convergence, etc.](46a17.md "MISSING PAGE")
                                  - [Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than bf R]$, etc.)](46a19.md "MISSING PAGE")
                                    [Duality theory](46a20.md "MISSING PAGE")
                                    [Theorems of Hahn-Banach type; extension and lifting of functionals and operators](46a22.md "MISSING PAGE")
                                    [Reflexivity and semi-reflexivity](46a25.md "MISSING PAGE")
                                    [Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)](46a30.md "MISSING PAGE")
                                    [Spaces of linear operators; topological tensor products; approximation properties](46a32.md "MISSING PAGE")
                                    [Summability and bases](46a35.md "MISSING PAGE")
                                    [Ordered topological linear spaces, vector lattices](46a40.md "MISSING PAGE")
                                    [Sequence spaces (including Köthe sequence spaces)](46a45.md "MISSING PAGE")
                                    [Compactness in topological linear spaces; angelic spaces, etc.](46a50.md "MISSING PAGE")
                                    [Convex sets in topological linear spaces; Choquet theory](46a55.md "MISSING PAGE")
                                    [Graded Fréchet spaces and tame operators](46a61.md "MISSING PAGE")
                                    [Topological invariants ((DN), ($Omega$), etc.)](46a63.md "MISSING PAGE")
                                    [Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)](46a70.md "MISSING PAGE")
                                    [Modular spaces](46a80.md "MISSING PAGE")
                                    [None of the above, but in this section](46a99.md "MISSING PAGE")
                                    [Normed linear spaces and Banach spaces; Banach lattices](46bxx.md "MISSING PAGE")
                                    [Isomorphic theory (including renorming) of Banach spaces](46b03.md "MISSING PAGE")
                                    [Isometric theory of Banach spaces](46b04.md "MISSING PAGE")
                                    [Local theory of Banach spaces](46b07.md "MISSING PAGE")
                                    [Ultraproduct techniques in Banach space theory](46b08.md "MISSING PAGE")
                                    [Probabilistic methods in Banach space theory](46b09.md "MISSING PAGE")
                                    [Duality and reflexivity](46b10.md "MISSING PAGE")
                                    [Summability and bases](46b15.md "MISSING PAGE")
                                    [Geometry and structure of normed linear spaces](46b20.md "MISSING PAGE")
                                    [Radon-Nikodym, Krein-Milman and related properties](46b22.md "MISSING PAGE")
                                    [Classical Banach spaces in the general theory](46b25.md "MISSING PAGE")
                                    [Nonseparable Banach spaces](46b26.md "MISSING PAGE")
                                    [Spaces of operators; tensor products; approximation properties](46b28.md "MISSING PAGE")
                                    [Ordered normed spaces](46b40.md "MISSING PAGE")
                                    [Banach lattices](46b42.md "MISSING PAGE")
                                    [Banach sequence spaces](46b45.md "MISSING PAGE")
                                    [Compactness in Banach (or normed) spaces](46b50.md "MISSING PAGE")
                                    [Interpolation between normed linear spaces](46b70.md "MISSING PAGE")
                                    [None of the above, but in this section](46b99.md "MISSING PAGE")
                                    [Inner product spaces and their generalizations, Hilbert spaces](46cxx.md "MISSING PAGE")
                                    [Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)](46c05.md "MISSING PAGE")
                                    [Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)](46c07.md "MISSING PAGE")
                                    [Characterizations of Hilbert spaces](46c15.md "MISSING PAGE")
                                    [Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.)](46c20.md "MISSING PAGE")
                                    [Generalizations of inner products (semi-inner products, partial inner products, etc.)](46c50.md "MISSING PAGE")
                                    [None of the above, but in this section](46c99.md "MISSING PAGE")
                                    [Linear function spaces and their duals](46exx.md "MISSING PAGE")
                                    [Lattices of continuous, differentiable or analytic functions](46e05.md "MISSING PAGE")
                                    [Topological linear spaces of continuous, differentiable or analytic functions](46e10.md "MISSING PAGE")
                                    [Banach spaces of continuous, differentiable or analytic functions](46e15.md "MISSING PAGE")
                                    [Hilbert spaces of continuous, differentiable or analytic functions](46e20.md "MISSING PAGE")
                                    [Hilbert spaces with reproducing kernels (= proper functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)](46e22.md "MISSING PAGE")
                                    [Rings and algebras of continuous, differentiable or analytic functions](46e25.md "MISSING PAGE")
                                    [Spaces of measures](46e27.md "MISSING PAGE")
                                    [Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)](46e30.md "MISSING PAGE")
                                    [Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems](46e35.md "MISSING PAGE")
                                    [Sobolev (and similar kinds of) spaces of functions of discrete variables](46e39.md "MISSING PAGE")
                                    [Spaces of vector- and operator-valued functions](46e40.md "MISSING PAGE")
                                    [Spaces of differentiable or holomorphic functions on infinite-dimensional spaces](46e50.md "MISSING PAGE")
                                    [None of the above, but in this section](46e99.md "MISSING PAGE")
                                    [Distributions, generalized functions, distribution spaces](46fxx.md "MISSING PAGE")
                                    [Topological linear spaces of test functions, distributions and ultradistributions](46f05.md "MISSING PAGE")
                                    [Operations with distributions](46f10.md "MISSING PAGE")
                                    [Integral transforms in distribution spaces](46f12.md "MISSING PAGE")
                                    [Hyperfunctions, analytic functionals](46f15.md "MISSING PAGE")
                                    [Distributions and ultradistributions as boundary values of analytic functions](46f20.md "MISSING PAGE")
                                    [Distributions on infinite-dimensional spaces](46f25.md "MISSING PAGE")
                                    [Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)](46f30.md "MISSING PAGE")
                                    [None of the above, but in this section](46f99.md "MISSING PAGE")
                                    [Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)](46gxx.md "MISSING PAGE")
                                    [Derivatives](46g05.md "MISSING PAGE")
                                    [Vector-valued measures and integration](46g10.md "MISSING PAGE")
                                    [Measures and integration on abstract linear spaces](46g12.md "MISSING PAGE")
                                    [Functional analytic lifting theory](46g15.md "MISSING PAGE")
                                    [Infinite-dimensional holomorphy](46g20.md "MISSING PAGE")
                                    [(Spaces of) multilinear mappings, polynomials](46g25.md "MISSING PAGE")
                                    [None of the above, but in this section](46g99.md "MISSING PAGE")
                                    [Topological algebras, normed rings and algebras, Banach algebras](46hxx.md "MISSING PAGE")
                                    [General theory of topological algebras](46h05.md "MISSING PAGE")
                                    [Ideals and subalgebras](46h10.md "MISSING PAGE")
                                    [Representations of topological algebras](46h15.md "MISSING PAGE")
                                    [Structure, classification of topological algebras](46h20.md "MISSING PAGE")
                                    [Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)](46h25.md "MISSING PAGE")
                                    [Functional calculus in topological algebras](46h30.md "MISSING PAGE")
                                    [Topological algebras of operators](46h35.md "MISSING PAGE")
                                    [Automatic continuity](46h40.md "MISSING PAGE")
                                    [Nonassociative topological algebras](46h70.md "MISSING PAGE")
                                    [None of the above, but in this section](46h99.md "MISSING PAGE")
                                    [Commutative Banach algebras and commutative topological algebras](46jxx.md "MISSING PAGE")
                                    [General theory of commutative topological algebras](46j05.md "MISSING PAGE")
                                    [Banach algebras of continuous functions, function algebras](46j10.md "MISSING PAGE")
                                    [Banach algebras of differentiable or analytic functions, H]^p$-spaces](46j15.md "MISSING PAGE")
                                    [Ideals, maximal ideals, boundaries](46j20.md "MISSING PAGE")
                                    [Representations of commutative topological algebras](46j25.md "MISSING PAGE")
                                    [Subalgebras](46j30.md "MISSING PAGE")
                                    [Structure, classification of commutative topological algebras](46j40.md "MISSING PAGE")
                                    [Radical Banach algebras](46j45.md "MISSING PAGE")
                                    [None of the above, but in this section](46j99.md "MISSING PAGE")
                                    [Topological (rings and) algebras with an involution](46kxx.md "MISSING PAGE")
                                    [General theory of topological algebras with involution](46k05.md "MISSING PAGE")
                                    [Representations of topological algebras with involution](46k10.md "MISSING PAGE")
                                    [Hilbert algebras](46k15.md "MISSING PAGE")
                                    [Nonselfadjoint (sub)algebras in algebras with involution](46k50.md "MISSING PAGE")
                                    [Nonassociative topological algebras with an involution](46k70.md "MISSING PAGE")
                                    [None of the above, but in this section](46k99.md "MISSING PAGE")
                                    [Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.)](46lxx.md "MISSING PAGE")
                                    [General theory of $C^*$-algebras](46l05.md "MISSING PAGE")
                                    [Tensor products of $C^*$-algebras](46l06.md "MISSING PAGE")
                                    [Operator spaces and completely bounded maps](46l07.md "MISSING PAGE")
                                    [$C^*$-modules](46l08.md "MISSING PAGE")
                                    [Free products of $C^*$-algebras](46l09.md "MISSING PAGE")
                                    [General theory of von Neumann algebras](46l10.md "MISSING PAGE")
                                    [States](46l30.md "MISSING PAGE")
                                    [Classifications of $C^*$-algebras, factors](46l35.md "MISSING PAGE")
                                    [Subfactors and their classification](46l37.md "MISSING PAGE")
                                    [Automorphisms](46l40.md "MISSING PAGE")
                                    [Decomposition theory for $C^*$-algebras](46l45.md "MISSING PAGE")
                                    [Noncommutative measure and integration](46l51.md "MISSING PAGE")
                                    [Noncommutative function spaces](46l52.md "MISSING PAGE")
                                    [Noncommutative probability and statistics](46l53.md "MISSING PAGE")
                                    [Free probability and free operator algebras](46l54.md "MISSING PAGE")
                                    [Noncommutative dynamical systems](46l55.md "MISSING PAGE")
                                    [Derivations, dissipations and positive semigroups in $C^*$-algebras](46l57.md "MISSING PAGE")
                                    [Applications of selfadjoint operator algebras to physics](46l60.md "MISSING PAGE")
                                    [Quantizations, deformations](46l65.md "MISSING PAGE")
                                    [Nonassociative selfadjoint operator algebras](46l70.md "MISSING PAGE")
                                    [$K$-theory and operator algebras (including cyclic theory)](46l80.md "MISSING PAGE")
                                    [Noncommutative topology](46l85.md "MISSING PAGE")
                                    [Noncommutative differential geometry](46l87.md "MISSING PAGE")
                                    [Other ``noncommutative'' mathematics based on $C^*$-algebra theory](46l89.md "MISSING PAGE")
                                    [None of the above, but in this section](46l99.md "MISSING PAGE")
                                    [Methods of category theory in functional analysis](46mxx.md "MISSING PAGE")
                                    [Tensor products](46m05.md "MISSING PAGE")
                                    [Ultraproducts](46m07.md "MISSING PAGE")
                                    [Projective and injective objects](46m10.md "MISSING PAGE")
                                    [Categories, functors](46m15.md "MISSING PAGE")
                                    [Homological methods (exact sequences, right inverses, lifting, etc.)](46m18.md "MISSING PAGE")
                                    [Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)](46m20.md "MISSING PAGE")
                                    [Abstract interpolation of topological vector spaces](46m35.md "MISSING PAGE")
                                    [Inductive and projective limits](46m40.md "MISSING PAGE")
                                    [None of the above, but in this section](46m99.md "MISSING PAGE")
                                    [Miscellaneous applications of functional analysis](46nxx.md "MISSING PAGE")
                                    [Applications in optimization, convex analysis, mathematical programming, economics](46n10.md "MISSING PAGE")
                                    [Applications to differential and integral equations](46n20.md "MISSING PAGE")
                                    [Applications in probability theory and statistics](46n30.md "MISSING PAGE")
                                    [Applications in numerical analysis](46n40.md "MISSING PAGE")
                                    [Applications in quantum physics](46n50.md "MISSING PAGE")
                                    [Applications in statistical physics](46n55.md "MISSING PAGE")
                                    [Applications in biology and other sciences](46n60.md "MISSING PAGE")
                                    [None of the above, but in this section](46n99.md "MISSING PAGE")
                                    [Other (nonclassical) types of functional analysis](46sxx.md "MISSING PAGE")
                                    [Functional analysis over fields other than <B>R</B> or <B>C</B> or the quaternions; non-Archimedean functional analysis](46s10.md "MISSING PAGE")
                                    [Nonstandard functional analysis](46s20.md "MISSING PAGE")
                                    [Constructive functional analysis](46s30.md "MISSING PAGE")
                                    [Fuzzy functional analysis](46s40.md "MISSING PAGE")
                                    [Functional analysis in probabilistic metric linear spaces](46s50.md "MISSING PAGE")
                                    [Functional analysis on superspaces (supermanifolds) or graded spaces](46s60.md "MISSING PAGE")
                                    [None of the above, but in this section](46s99.md "MISSING PAGE")
                                    [Nonlinear functional analysis](46txx.md "MISSING PAGE")
                                    [Infinite-dimensional manifolds](46t05.md "MISSING PAGE")
                                    [Manifolds of mappings](46t10.md "MISSING PAGE")
                                    [Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds](46t12.md "MISSING PAGE")
                                    [Continuous and differentiable maps](46t20.md "MISSING PAGE")
                                    [Holomorphic maps](46t25.md "MISSING PAGE")
                                    [Distributions and generalized functions on nonlinear spaces](46t30.md "MISSING PAGE")
                                    [None of the above, but in this section](46t99.md "MISSING PAGE")
                                    ## [Operator theory](47-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](47-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](47-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](47-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](47-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](47-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](47-06.md "MISSING PAGE")
                                                - [General theory of linear operators](47axx.md "MISSING PAGE")
                                                - [General (adjoints, conjugates, products, inverses, domains, ranges, etc.)](47a05.md "MISSING PAGE")
                                                - [Linear relations (multivalued linear operators)](47a06.md "MISSING PAGE")
                                                - [Forms (bilinear, sesquilinear, multilinear)](47a07.md "MISSING PAGE")
                                                - [Spectrum, resolvent](47a10.md "MISSING PAGE")
                                                - [Local spectral properties](47a11.md "MISSING PAGE")
                                                - [Numerical range, numerical radius](47a12.md "MISSING PAGE")
                                                - [Several-variable operator theory (spectral, Fredholm, etc.)](47a13.md "MISSING PAGE")
                                                - [Invariant subspaces](47a15.md "MISSING PAGE")
                                                - [Cyclic and hypercyclic vectors](47a16.md "MISSING PAGE")
                                                - [Dilations, extensions, compressions](47a20.md "MISSING PAGE")
                                                - [Spectral sets](47a25.md "MISSING PAGE")
                                                - [Norms (inequalities, more than one norm, etc.)](47a30.md "MISSING PAGE")
                                                - [Ergodic theory](47a35.md "MISSING PAGE")
                                                - [Scattering theory](47a40.md "MISSING PAGE")
                                                - [Canonical models for contractions and nonselfadjoint operators](47a45.md "MISSING PAGE")
                                                - [Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.](47a46.md "MISSING PAGE")
                                                - [Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.](47a48.md "MISSING PAGE")
                                                - [Equations and inequalities involving linear operators, with vector unknowns](47a50.md "MISSING PAGE")
                                                - [Ill-posed problems, regularization](47a52.md "MISSING PAGE")
                                                - [(Semi-) Fredholm operators; index theories](47a53.md "MISSING PAGE")
                                                - [Perturbation theory](47a55.md "MISSING PAGE")
                                                - [Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)](47a56.md "MISSING PAGE")
                                                - [Operator methods in interpolation, moment and extension problems](47a57.md "MISSING PAGE")
                                                - [Operator approximation theory](47a58.md "MISSING PAGE")
                                                - [Functional calculus](47a60.md "MISSING PAGE")
                                                - [Equations involving linear operators, with operator unknowns](47a62.md "MISSING PAGE")
                                                - [Operator inequalities](47a63.md "MISSING PAGE")
                                                - [Operator means, shorted operators, etc.](47a64.md "MISSING PAGE")
                                                - [Structure theory](47a65.md "MISSING PAGE")
                                                - [Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators](47a66.md "MISSING PAGE")
                                                - [Representation theory](47a67.md "MISSING PAGE")
                                                - [Factorization theory (including Wiener-Hopf and spectral factorizations)](47a68.md "MISSING PAGE")
                                                - [(Generalized) eigenfunction expansions; rigged Hilbert spaces](47a70.md "MISSING PAGE")
                                                - [Eigenvalue problems](47a75.md "MISSING PAGE")
                                                - [Tensor products of operators](47a80.md "MISSING PAGE")
                                                - [None of the above, but in this section](47a99.md "MISSING PAGE")
                                                - [Special classes of linear operators](47bxx.md "MISSING PAGE")
                                                - [Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators](47b06.md "MISSING PAGE")
                                                - [Operators defined by compactness properties](47b07.md "MISSING PAGE")
                                                - [Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)](47b10.md "MISSING PAGE")
                                                - [Hermitian and normal operators (spectral measures, functional calculus, etc.)](47b15.md "MISSING PAGE")
                                                - [Subnormal operators, hyponormal operators, etc.](47b20.md "MISSING PAGE")
                                                - [Symmetric and selfadjoint operators (unbounded)](47b25.md "MISSING PAGE")
                                                - [Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)](47b32.md "MISSING PAGE")
                                                - [Composition operators](47b33.md "MISSING PAGE")
                                                - [Kernel operators](47b34.md "MISSING PAGE")
                                                - [Toeplitz operators, Hankel operators, Wiener-Hopf operators](47b35.md "MISSING PAGE")
                                                - [Jacobi (tridiagonal) operators (matrices) and generalizations](47b36.md "MISSING PAGE")
                                                - [Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)](47b37.md "MISSING PAGE")
                                                - [Operators on function spaces (general)](47b38.md "MISSING PAGE")
                                                - [Difference operators](47b39.md "MISSING PAGE")
                                                - [Spectral operators, decomposable operators, well-bounded operators, etc.](47b40.md "MISSING PAGE")
                                                - [Accretive operators, dissipative operators, etc.](47b44.md "MISSING PAGE")
                                                - [Commutators, derivations, elementary operators, etc.](47b47.md "MISSING PAGE")
                                                - [Operators on Banach algebras](47b48.md "MISSING PAGE")
                                                - [Transformers (= operators on spaces of operators)](47b49.md "MISSING PAGE")
                                                - [Operators on spaces with an indefinite metric](47b50.md "MISSING PAGE")
                                                - [Operators on ordered spaces](47b60.md "MISSING PAGE")
                                                - [Positive operators and order-bounded operators](47b65.md "MISSING PAGE")
                                                - [Random operators](47b80.md "MISSING PAGE")
                                                - [None of the above, but in this section](47b99.md "MISSING PAGE")
                                                - [Individual linear operators as elements of algebraic systems](47cxx.md "MISSING PAGE")
                                                - [Operators in algebras](47c05.md "MISSING PAGE")
                                                - [Operators in $^*$-algebras](47c10.md "MISSING PAGE")
                                                - [Operators in $C^*$- or von Neumann algebras](47c15.md "MISSING PAGE")
                                                - [None of the above, but in this section](47c99.md "MISSING PAGE")
                                                - [Groups and semigroups of linear operators, their generalizations and applications](47dxx.md "MISSING PAGE")
                                                - [Groups and semigroups of linear operators](47d03.md "MISSING PAGE")
                                                - [One-parameter semigroups and linear evolution equations](47d06.md "MISSING PAGE")
                                                - [Markov semigroups and applications to diffusion processes](47d07.md "MISSING PAGE")
                                                - [Schrödinger and Feynman-Kac semigroups](47d08.md "MISSING PAGE")
                                                - [Operator sine and cosine functions and higher-order Cauchy problems](47d09.md "MISSING PAGE")
                                                - [$C$-semigroups](47d60.md "MISSING PAGE")
                                                - [Integrated semigroups](47d62.md "MISSING PAGE")
                                                - [None of the above, but in this section](47d99.md "MISSING PAGE")
                                                - [Ordinary differential operators](47e05.md "MISSING PAGE")
                                                - [Partial differential operators](47f05.md "MISSING PAGE")
                                                - [Integral, integro-differential, and pseudodifferential operators](47gxx.md "MISSING PAGE")
                                                - [Integral operators](47g10.md "MISSING PAGE")
                                                - [Integro-differential operators](47g20.md "MISSING PAGE")
                                                - [Pseudodifferential operators](47g30.md "MISSING PAGE")
                                                - [None of the above, but in this section](47g99.md "MISSING PAGE")
                                                - [Nonlinear operators and their properties](47hxx.md "MISSING PAGE")
                                                - [Set-valued operators](47h04.md "MISSING PAGE")
                                                - [Monotone operators (with respect to duality)](47h05.md "MISSING PAGE")
                                                - [Accretive operators, dissipative operators, etc.](47h06.md "MISSING PAGE")
                                                - [Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces](47h07.md "MISSING PAGE")
                                                - [Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.)](47h09.md "MISSING PAGE")
                                                - [Fixed-point theorems](47h10.md "MISSING PAGE")
                                                - [Degree theory](47h11.md "MISSING PAGE")
                                                - [Perturbations of nonlinear operators](47h14.md "MISSING PAGE")
                                                - [Semigroups of nonlinear operators](47h20.md "MISSING PAGE")
                                                - [Particular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.)](47h30.md "MISSING PAGE")
                                                - [Random operators](47h40.md "MISSING PAGE")
                                                - [Potential operators](47h50.md "MISSING PAGE")
                                                - [Multilinear and polynomial operators](47h60.md "MISSING PAGE")
                                                - [None of the above, but in this section](47h99.md "MISSING PAGE")
                                                - [Equations and inequalities involving nonlinear operators](47jxx.md "MISSING PAGE")
                                                - [Equations involving nonlinear operators (general)](47j05.md "MISSING PAGE")
                                                - [Nonlinear ill-posed problems](47j06.md "MISSING PAGE")
                                                - [Abstract inverse mapping and implicit function theorems](47j07.md "MISSING PAGE")
                                                - [Nonlinear eigenvalue problems](47j10.md "MISSING PAGE")
                                                - [Abstract bifurcation theory](47j15.md "MISSING PAGE")
                                                - [Variational and other types of inequalities involving nonlinear operators (general)](47j20.md "MISSING PAGE")
                                                - [Methods for solving nonlinear operator equations (general)](47j25.md "MISSING PAGE")
                                                - [Variational methods](47j30.md "MISSING PAGE")
                                                - [Nonlinear evolution equations](47j35.md "MISSING PAGE")
                                                - [Equations with hysteresis operators](47j40.md "MISSING PAGE")
                                                - [None of the above, but in this section](47j99.md "MISSING PAGE")
                                                - [Linear spaces and algebras of operators](47lxx.md "MISSING PAGE")
                                                - [Linear spaces of operators](47l05.md "MISSING PAGE")
                                                - [Convex sets and cones of operators](47l07.md "MISSING PAGE")
                                                - [Algebras of operators on Banach spaces and other topological linear spaces](47l10.md "MISSING PAGE")
                                                - [Operator algebras with symbol structure](47l15.md "MISSING PAGE")
                                                - [Operator ideals](47l20.md "MISSING PAGE")
                                                - [Operator spaces (= matricially normed spaces)](47l25.md "MISSING PAGE")
                                                - [Abstract operator algebras on Hilbert spaces](47l30.md "MISSING PAGE")
                                                - [Nest algebras, CSL algebras](47l35.md "MISSING PAGE")
                                                - [Limit algebras, subalgebras of $C^*$-algebras](47l40.md "MISSING PAGE")
                                                - [Dual algebras; weakly closed singly generated operator algebras](47l45.md "MISSING PAGE")
                                                - [Dual spaces of operator algebras](47l50.md "MISSING PAGE")
                                                - [Representations of (nonselfadjoint) operator algebras](47l55.md "MISSING PAGE")
                                                - [Algebras of unbounded operators; partial algebras of operators](47l60.md "MISSING PAGE")
                                                - [Crossed product algebras (analytic crossed products)](47l65.md "MISSING PAGE")
                                                - [Nonassociative nonselfadjoint operator algebras](47l70.md "MISSING PAGE")
                                                - [Other nonselfadjoint operator algebras](47l75.md "MISSING PAGE")
                                                - [Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)](47l80.md "MISSING PAGE")
                                                - [Applications of operator algebras to physics](47l90.md "MISSING PAGE")
                                                - [None of the above, but in this section](47l99.md "MISSING PAGE")
                                                - [Miscellaneous applications of operator theory](47nxx.md "MISSING PAGE")
                                                - [Applications in optimization, convex analysis, mathematical programming, economics](47n10.md "MISSING PAGE")
                                                - [Applications to differential and integral equations](47n20.md "MISSING PAGE")
                                                - [Applications in probability theory and statistics](47n30.md "MISSING PAGE")
                                                - [Applications in numerical analysis](47n40.md "MISSING PAGE")
                                                - [Applications in quantum physics](47n50.md "MISSING PAGE")
                                                - [Applications in statistical physics](47n55.md "MISSING PAGE")
                                                - [Applications in biology and other sciences](47n60.md "MISSING PAGE")
                                                - [Applications in systems theory, circuits, etc.](47n70.md "MISSING PAGE")
                                                - [None of the above, but in this section](47n99.md "MISSING PAGE")
                                                - [Other (nonclassical) types of operator theory](47sxx.md "MISSING PAGE")
                                                - [Operator theory over fields other than <B>R</B>, <B>C</B> or the quaternions; non-Archimedean operator theory](47s10.md "MISSING PAGE")
                                                - [Nonstandard operator theory](47s20.md "MISSING PAGE")
                                                - [Constructive operator theory](47s30.md "MISSING PAGE")
                                                - [Fuzzy operator theory](47s40.md "MISSING PAGE")
                                                - [Operator theory in probabilistic metric linear spaces](47s50.md "MISSING PAGE")
                                                - [None of the above, but in this section](47s99.md "MISSING PAGE")
                                    ## [Calculus of variations and optimal control; optimization](49-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](49-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](49-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](49-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](49-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](49-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](49-06.md "MISSING PAGE")
                                                - [Existence theories](49jxx.md "MISSING PAGE")
                                                - [Free problems in one independent variable](49j05.md "MISSING PAGE")
                                                - [Free problems in two or more independent variables](49j10.md "MISSING PAGE")
                                                - [Optimal control problems involving ordinary differential equations](49j15.md "MISSING PAGE")
                                                - [Optimal control problems involving partial differential equations](49j20.md "MISSING PAGE")
                                                - [Optimal control problems involving integral equations](49j22.md "MISSING PAGE")
                                                - [Optimal control problems involving differential inclusions](49j24.md "MISSING PAGE")
                                                - [Optimal control problems involving equations with retarded arguments](49j25.md "MISSING PAGE")
                                                - [Problems in abstract spaces](49j27.md "MISSING PAGE")
                                                - [Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)](49j30.md "MISSING PAGE")
                                                - [Minimax problems](49j35.md "MISSING PAGE")
                                                - [Variational methods including variational inequalities](49j40.md "MISSING PAGE")
                                                - [Methods involving semicontinuity and convergence; relaxation](49j45.md "MISSING PAGE")
                                                - [Fréchet and Gateaux differentiability](49j50.md "MISSING PAGE")
                                                - [Nonsmooth analysis](49j52.md "MISSING PAGE")
                                                - [Set-valued and variational analysis](49j53.md "MISSING PAGE")
                                                - [Problems involving randomness](49j55.md "MISSING PAGE")
                                                - [None of the above, but in this section](49j99.md "MISSING PAGE")
                                                - [Necessary conditions and sufficient conditions for optimality](49kxx.md "MISSING PAGE")
                                                - [Free problems in one independent variable](49k05.md "MISSING PAGE")
                                                - [Free problems in two or more independent variables](49k10.md "MISSING PAGE")
                                                - [Problems involving ordinary differential equations](49k15.md "MISSING PAGE")
                                                - [Problems involving partial differential equations](49k20.md "MISSING PAGE")
                                                - [Problems involving integral equations](49k22.md "MISSING PAGE")
                                                - [Problems involving differential inclusions](49k24.md "MISSING PAGE")
                                                - [Problems involving equations with retarded arguments](49k25.md "MISSING PAGE")
                                                - [Problems in abstract spaces](49k27.md "MISSING PAGE")
                                                - [Optimal solutions belonging to restricted classes](49k30.md "MISSING PAGE")
                                                - [Minimax problems](49k35.md "MISSING PAGE")
                                                - [Sensitivity, stability, well-posedness](49k40.md "MISSING PAGE")
                                                - [Problems involving randomness](49k45.md "MISSING PAGE")
                                                - [None of the above, but in this section](49k99.md "MISSING PAGE")
                                                - [Hamilton-Jacobi theories, including dynamic programming](49lxx.md "MISSING PAGE")
                                                - [Dynamic programming method](49l20.md "MISSING PAGE")
                                                - [Viscosity solutions](49l25.md "MISSING PAGE")
                                                - [None of the above, but in this section](49l99.md "MISSING PAGE")
                                                - [Methods of successive approximations](49mxx.md "MISSING PAGE")
                                                - [Methods based on necessary conditions](49m05.md "MISSING PAGE")
                                                - [Methods of Newton-Raphson, Galerkin and Ritz types](49m15.md "MISSING PAGE")
                                                - [Methods of relaxation type](49m20.md "MISSING PAGE")
                                                - [Discrete approximations](49m25.md "MISSING PAGE")
                                                - [Decomposition methods](49m27.md "MISSING PAGE")
                                                - [Methods involving duality](49m29.md "MISSING PAGE")
                                                - [Other methods, not based on necessary conditions (penalty function, etc.)](49m30.md "MISSING PAGE")
                                                - [Methods of nonlinear programming type](49m37.md "MISSING PAGE")
                                                - [None of the above, but in this section](49m99.md "MISSING PAGE")
                                                - [Miscellaneous topics](49nxx.md "MISSING PAGE")
                                                - [Linear optimal control problems](49n05.md "MISSING PAGE")
                                                - [Linear-quadratic problems](49n10.md "MISSING PAGE")
                                                - [Duality theory](49n15.md "MISSING PAGE")
                                                - [Periodic optimization](49n20.md "MISSING PAGE")
                                                - [Impulsive optimal control problems](49n25.md "MISSING PAGE")
                                                - [Problems with incomplete information](49n30.md "MISSING PAGE")
                                                - [Optimal feedback synthesis](49n35.md "MISSING PAGE")
                                                - [Inverse problems](49n45.md "MISSING PAGE")
                                                - [Regularity of solutions](49n60.md "MISSING PAGE")
                                                - [Differential games](49n70.md "MISSING PAGE")
                                                - [Pursuit and evasion games](49n75.md "MISSING PAGE")
                                                - [Applications of optimal control and differential games](49n90.md "MISSING PAGE")
                                                - [None of the above, but in this section](49n99.md "MISSING PAGE")
                                                - [Manifolds](49qxx.md "MISSING PAGE")
                                                - [Minimal surfaces](49q05.md "MISSING PAGE")
                                                - [Optimization of shapes other than minimal surfaces](49q10.md "MISSING PAGE")
                                                - [Sensitivity analysis](49q12.md "MISSING PAGE")
                                                - [Geometric measure and integration theory, integral and normal currents](49q15.md "MISSING PAGE")
                                                - [Variational problems in a geometric measure-theoretic setting](49q20.md "MISSING PAGE")
                                                - [None of the above, but in this section](49q99.md "MISSING PAGE")
                                                - [Variational methods for eigenvalues of operators](49r50.md "MISSING PAGE")
                                                - [Variational principles of physics](49s05.md "MISSING PAGE")
                                    ## [Geometry](51-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](51-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](51-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](51-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](51-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](51-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](51-06.md "MISSING PAGE")
                                                - [Linear incidence geometry](51axx.md "MISSING PAGE")
                                                - [General theory and projective geometries](51a05.md "MISSING PAGE")
                                                - [Homomorphism, automorphism and dualities](51a10.md "MISSING PAGE")
                                                - [Structures with parallelism](51a15.md "MISSING PAGE")
                                                - [Configuration theorems](51a20.md "MISSING PAGE")
                                                - [Algebraization](51a25.md "MISSING PAGE")
                                                - [Desarguesian and Pappian geometries](51a30.md "MISSING PAGE")
                                                - [Non-Desarguesian affine and projective planes](51a35.md "MISSING PAGE")
                                                - [Translation planes and spreads](51a40.md "MISSING PAGE")
                                                - [Incidence structures imbeddable into projective geometries](51a45.md "MISSING PAGE")
                                                - [Polar geometry, symplectic spaces, orthogonal spaces](51a50.md "MISSING PAGE")
                                                - [None of the above, but in this section](51a99.md "MISSING PAGE")
                                                - [Nonlinear incidence geometry](51bxx.md "MISSING PAGE")
                                                - [General theory](51b05.md "MISSING PAGE")
                                                - [Möbius geometries](51b10.md "MISSING PAGE")
                                                - [Laguerre geometries](51b15.md "MISSING PAGE")
                                                - [Minkowski geometries](51b20.md "MISSING PAGE")
                                                - [Lie geometries](51b25.md "MISSING PAGE")
                                                - [None of the above, but in this section](51b99.md "MISSING PAGE")
                                                - [Ring geometry (Hjelmslev, Barbilian, etc.)](51c05.md "MISSING PAGE")
                                                - [Geometric closure systems](51dxx.md "MISSING PAGE")
                                                - [Abstract (Maeda) geometries](51d05.md "MISSING PAGE")
                                                - [Abstract geometries with exchange axiom](51d10.md "MISSING PAGE")
                                                - [Abstract geometries with parallelism](51d15.md "MISSING PAGE")
                                                - [Combinatorial geometries](51d20.md "MISSING PAGE")
                                                - [Lattices of subspaces](51d25.md "MISSING PAGE")
                                                - [Continuous geometries and related topics](51d30.md "MISSING PAGE")
                                                - [None of the above, but in this section](51d99.md "MISSING PAGE")
                                                - [Finite geometry and special incidence structures](51exx.md "MISSING PAGE")
                                                - [General block designs](51e05.md "MISSING PAGE")
                                                - [Steiner systems](51e10.md "MISSING PAGE")
                                                - [Generalized quadrangles, generalized polygons](51e12.md "MISSING PAGE")
                                                - [Finite partial geometries (general), nets, partial spreads](51e14.md "MISSING PAGE")
                                                - [Affine and projective planes](51e15.md "MISSING PAGE")
                                                - [Combinatorial structures in finite projective spaces](51e20.md "MISSING PAGE")
                                                - [Blocking sets, ovals, $k$-arcs](51e21.md "MISSING PAGE")
                                                - [Linear codes and caps in Galois spaces](51e22.md "MISSING PAGE")
                                                - [Spreads and packing problems](51e23.md "MISSING PAGE")
                                                - [Buildings and the geometry of diagrams](51e24.md "MISSING PAGE")
                                                - [Other finite nonlinear geometries](51e25.md "MISSING PAGE")
                                                - [Other finite linear geometries](51e26.md "MISSING PAGE")
                                                - [Other finite incidence structures](51e30.md "MISSING PAGE")
                                                - [None of the above, but in this section](51e99.md "MISSING PAGE")
                                                - [Metric geometry](51fxx.md "MISSING PAGE")
                                                - [Absolute planes](51f05.md "MISSING PAGE")
                                                - [Absolute spaces](51f10.md "MISSING PAGE")
                                                - [Reflection groups, reflection geometries](51f15.md "MISSING PAGE")
                                                - [Congruence and orthogonality](51f20.md "MISSING PAGE")
                                                - [Orthogonal and unitary groups](51f25.md "MISSING PAGE")
                                                - [None of the above, but in this section](51f99.md "MISSING PAGE")
                                                - [Ordered geometries (ordered incidence structures, etc.)](51g05.md "MISSING PAGE")
                                                - [Topological geometry](51hxx.md "MISSING PAGE")
                                                - [General theory](51h05.md "MISSING PAGE")
                                                - [Topological linear incidence structures](51h10.md "MISSING PAGE")
                                                - [Topological nonlinear incidence structures](51h15.md "MISSING PAGE")
                                                - [Topological geometries on manifolds](51h20.md "MISSING PAGE")
                                                - [Geometries with differentiable structure](51h25.md "MISSING PAGE")
                                                - [Geometries with algebraic manifold structure](51h30.md "MISSING PAGE")
                                                - [None of the above, but in this section](51h99.md "MISSING PAGE")
                                                - [Incidence groups](51jxx.md "MISSING PAGE")
                                                - [General theory](51j05.md "MISSING PAGE")
                                                - [Projective incidence groups](51j10.md "MISSING PAGE")
                                                - [Kinematic spaces](51j15.md "MISSING PAGE")
                                                - [Representation by near-fields and near-algebras](51j20.md "MISSING PAGE")
                                                - [None of the above, but in this section](51j99.md "MISSING PAGE")
                                                - [Distance geometry](51kxx.md "MISSING PAGE")
                                                - [General theory](51k05.md "MISSING PAGE")
                                                - [Synthetic differential geometry](51k10.md "MISSING PAGE")
                                                - [None of the above, but in this section](51k99.md "MISSING PAGE")
                                                - [Geometric order structures](51lxx.md "MISSING PAGE")
                                                - [Geometry of orders of nondifferentiable curves](51l05.md "MISSING PAGE")
                                                - [Directly differentiable curves](51l10.md "MISSING PAGE")
                                                - [$n$-vertex theorems via direct methods](51l15.md "MISSING PAGE")
                                                - [Geometry of orders of surfaces](51l20.md "MISSING PAGE")
                                                - [None of the above, but in this section](51l99.md "MISSING PAGE")
                                                - [Real and complex geometry](51mxx.md "MISSING PAGE")
                                                - [Elementary problems in Euclidean geometries](51m04.md "MISSING PAGE")
                                                - [Euclidean geometries (general) and generalizations](51m05.md "MISSING PAGE")
                                                - [Elementary problems in hyperbolic and elliptic geometries](51m09.md "MISSING PAGE")
                                                - [Hyperbolic and elliptic geometries (general) and generalizations](51m10.md "MISSING PAGE")
                                                - [Geometric constructions](51m15.md "MISSING PAGE")
                                                - [Inequalities and extremum problems](51m16.md "MISSING PAGE")
                                                - [Polyhedra and polytopes; regular figures, division of spaces](51m20.md "MISSING PAGE")
                                                - [Length, area and volume](51m25.md "MISSING PAGE")
                                                - [Line geometries and their generalizations](51m30.md "MISSING PAGE")
                                                - [Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)](51m35.md "MISSING PAGE")
                                                - [None of the above, but in this section](51m99.md "MISSING PAGE")
                                                - [Analytic and descriptive geometry](51nxx.md "MISSING PAGE")
                                                - [Descriptive geometry](51n05.md "MISSING PAGE")
                                                - [Affine analytic geometry](51n10.md "MISSING PAGE")
                                                - [Projective analytic geometry](51n15.md "MISSING PAGE")
                                                - [Euclidean analytic geometry](51n20.md "MISSING PAGE")
                                                - [Analytic geometry with other transformation groups](51n25.md "MISSING PAGE")
                                                - [Geometry of classical groups](51n30.md "MISSING PAGE")
                                                - [Questions of classical algebraic geometry](51n35.md "MISSING PAGE")
                                                - [None of the above, but in this section](51n99.md "MISSING PAGE")
                                                - [Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)](51p05.md "MISSING PAGE")
                                    ## [Convex and discrete geometry](52-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](52-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](52-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](52-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](52-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](52-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](52-06.md "MISSING PAGE")
                                                - [General convexity](52axx.md "MISSING PAGE")
                                                - [Axiomatic and generalized convexity](52a01.md "MISSING PAGE")
                                                - [Convex sets without dimension restrictions](52a05.md "MISSING PAGE")
                                                - [Convex sets in topological vector spaces](52a07.md "MISSING PAGE")
                                                - [Convex sets in $2$ dimensions (including convex curves)](52a10.md "MISSING PAGE")
                                                - [Convex sets in $3$ dimensions (including convex surfaces)](52a15.md "MISSING PAGE")
                                                - [Convex sets in $n$ dimensions (including convex hypersurfaces)](52a20.md "MISSING PAGE")
                                                - [Finite-dimensional Banach spaces (including special norms, zonoids, etc.)](52a21.md "MISSING PAGE")
                                                - [Random convex sets and integral geometry](52a22.md "MISSING PAGE")
                                                - [Approximation by convex sets](52a27.md "MISSING PAGE")
                                                - [Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)](52a30.md "MISSING PAGE")
                                                - [Helly-type theorems and geometric transversal theory](52a35.md "MISSING PAGE")
                                                - [Other problems of combinatorial convexity](52a37.md "MISSING PAGE")
                                                - [Length, area, volume](52a38.md "MISSING PAGE")
                                                - [Mixed volumes and related topics](52a39.md "MISSING PAGE")
                                                - [Inequalities and extremum problems](52a40.md "MISSING PAGE")
                                                - [Convex functions and convex programs](52a41.md "MISSING PAGE")
                                                - [Spherical and hyperbolic convexity](52a55.md "MISSING PAGE")
                                                - [None of the above, but in this section](52a99.md "MISSING PAGE")
                                                - [Polytopes and polyhedra](52bxx.md "MISSING PAGE")
                                                - [Combinatorial properties (number of faces, shortest paths, etc.)](52b05.md "MISSING PAGE")
                                                - [Three-dimensional polytopes](52b10.md "MISSING PAGE")
                                                - [$n$-dimensional polytopes](52b11.md "MISSING PAGE")
                                                - [Special polytopes (linear programming, centrally symmetric, etc.)](52b12.md "MISSING PAGE")
                                                - [Symmetry properties of polytopes](52b15.md "MISSING PAGE")
                                                - [Lattice polytopes (including relations with commutative algebra and algebraic geometry)](52b20.md "MISSING PAGE")
                                                - [Shellability](52b22.md "MISSING PAGE")
                                                - [Gale and other diagrams](52b35.md "MISSING PAGE")
                                                - [Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)](52b40.md "MISSING PAGE")
                                                - [Dissections and valuations (Hilbert's third problem, etc.)](52b45.md "MISSING PAGE")
                                                - [Computational aspects related to convexity](52b55.md "MISSING PAGE")
                                                - [Isoperimetric problems for polytopes](52b60.md "MISSING PAGE")
                                                - [Polyhedral manifolds](52b70.md "MISSING PAGE")
                                                - [None of the above, but in this section](52b99.md "MISSING PAGE")
                                                - [Discrete geometry](52cxx.md "MISSING PAGE")
                                                - [Lattices and convex bodies in $2$ dimensions](52c05.md "MISSING PAGE")
                                                - [Lattices and convex bodies in $n$ dimensions](52c07.md "MISSING PAGE")
                                                - [Erdös problems and related topics of discrete geometry](52c10.md "MISSING PAGE")
                                                - [Packing and covering in $2$ dimensions](52c15.md "MISSING PAGE")
                                                - [Packing and covering in $n$ dimensions](52c17.md "MISSING PAGE")
                                                - [Tilings in $2$ dimensions](52c20.md "MISSING PAGE")
                                                - [Tilings in $n$ dimensions](52c22.md "MISSING PAGE")
                                                - [Quasicrystals, aperiodic tilings](52c23.md "MISSING PAGE")
                                                - [Rigidity and flexibility of structures](52c25.md "MISSING PAGE")
                                                - [Circle packings and discrete conformal geometry](52c26.md "MISSING PAGE")
                                                - [Planar arrangements of lines and pseudolines](52c30.md "MISSING PAGE")
                                                - [Arrangements of points, flats, hyperplanes](52c35.md "MISSING PAGE")
                                                - [Oriented matroids](52c40.md "MISSING PAGE")
                                                - [Combinatorial complexity of geometric structures](52c45.md "MISSING PAGE")
                                                - [None of the above, but in this section](52c99.md "MISSING PAGE")
                                    ## [Differential geometry](53-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](53-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](53-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](53-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](53-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](53-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](53-06.md "MISSING PAGE")
                                                - [Classical differential geometry](53axx.md "MISSING PAGE")
                                                - [Curves in Euclidean space](53a04.md "MISSING PAGE")
                                                - [Surfaces in Euclidean space](53a05.md "MISSING PAGE")
                                                - [Higher-dimensional and -codimensional surfaces in Euclidean $n$-space](53a07.md "MISSING PAGE")
                                                - [Minimal surfaces, surfaces with prescribed mean curvature](53a10.md "MISSING PAGE")
                                                - [Affine differential geometry](53a15.md "MISSING PAGE")
                                                - [Kinematics](53a17.md "MISSING PAGE")
                                                - [Projective differential geometry](53a20.md "MISSING PAGE")
                                                - [Differential line geometry](53a25.md "MISSING PAGE")
                                                - [Conformal differential geometry](53a30.md "MISSING PAGE")
                                                - [Non-Euclidean differential geometry](53a35.md "MISSING PAGE")
                                                - [Other special differential geometries](53a40.md "MISSING PAGE")
                                                - [Vector and tensor analysis](53a45.md "MISSING PAGE")
                                                - [Differential invariants (local theory), geometric objects](53a55.md "MISSING PAGE")
                                                - [Geometry of webs](53a60.md "MISSING PAGE")
                                                - [None of the above, but in this section](53a99.md "MISSING PAGE")
                                                - [Local differential geometry](53bxx.md "MISSING PAGE")
                                                - [Linear and affine connections](53b05.md "MISSING PAGE")
                                                - [Projective connections](53b10.md "MISSING PAGE")
                                                - [Other connections](53b15.md "MISSING PAGE")
                                                - [Local Riemannian geometry](53b20.md "MISSING PAGE")
                                                - [Methods of Riemannian geometry](53b21.md "MISSING PAGE")
                                                - [Local submanifolds](53b25.md "MISSING PAGE")
                                                - [Lorentz metrics, indefinite metrics](53b30.md "MISSING PAGE")
                                                - [Hermitian and Kählerian structures](53b35.md "MISSING PAGE")
                                                - [Finsler spaces and generalizations (areal metrics)](53b40.md "MISSING PAGE")
                                                - [Applications to physics](53b50.md "MISSING PAGE")
                                                - [None of the above, but in this section](53b99.md "MISSING PAGE")
                                                - [Global differential geometry](53cxx.md "MISSING PAGE")
                                                - [Connections, general theory](53c05.md "MISSING PAGE")
                                                - [Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)](53c07.md "MISSING PAGE")
                                                - [$G$-structures](53c10.md "MISSING PAGE")
                                                - [Foliations (differential geometric aspects)](53c12.md "MISSING PAGE")
                                                - [General geometric structures on manifolds (almost complex, almost product structures, etc.)](53c15.md "MISSING PAGE")
                                                - [Sub-Riemannian geometry](53c17.md "MISSING PAGE")
                                                - [Global Riemannian geometry, including pinching](53c20.md "MISSING PAGE")
                                                - [Methods of Riemannian geometry, including PDE methods; curvature restrictions](53c21.md "MISSING PAGE")
                                                - [Geodesics](53c22.md "MISSING PAGE")
                                                - [Global topological methods (à la Gromov)](53c23.md "MISSING PAGE")
                                                - [Rigidity results](53c24.md "MISSING PAGE")
                                                - [Special Riemannian manifolds (Einstein, Sasakian, etc.)](53c25.md "MISSING PAGE")
                                                - [Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry](53c26.md "MISSING PAGE")
                                                - [Spin and Spin$^c$ geometry](53c27.md "MISSING PAGE")
                                                - [Twistor methods](53c28.md "MISSING PAGE")
                                                - [Issues of holonomy](53c29.md "MISSING PAGE")
                                                - [Homogeneous manifolds](53c30.md "MISSING PAGE")
                                                - [Symmetric spaces](53c35.md "MISSING PAGE")
                                                - [Calibrations and calibrated geometries](53c38.md "MISSING PAGE")
                                                - [Global submanifolds](53c40.md "MISSING PAGE")
                                                - [Immersions (minimal, prescribed curvature, tight, etc.)](53c42.md "MISSING PAGE")
                                                - [Differential geometric aspects of harmonic maps](53c43.md "MISSING PAGE")
                                                - [Geometric evolution equations (mean curvature flow)](53c44.md "MISSING PAGE")
                                                - [Global surface theory (convex surfaces à la A. D. Aleksandrov)](53c45.md "MISSING PAGE")
                                                - [Lorentz manifolds, manifolds with indefinite metrics](53c50.md "MISSING PAGE")
                                                - [Hermitian and Kählerian manifolds](53c55.md "MISSING PAGE")
                                                - [Other complex differential geometry](53c56.md "MISSING PAGE")
                                                - [Finsler spaces and generalizations (areal metrics)](53c60.md "MISSING PAGE")
                                                - [Integral geometry; differential forms, currents, etc.](53c65.md "MISSING PAGE")
                                                - [Direct methods ($G$-spaces of Busemann, etc.)](53c70.md "MISSING PAGE")
                                                - [Geometric orders, order geometry](53c75.md "MISSING PAGE")
                                                - [Applications to physics](53c80.md "MISSING PAGE")
                                                - [None of the above, but in this section](53c99.md "MISSING PAGE")
                                                - [Symplectic geometry, contact geometry](53dxx.md "MISSING PAGE")
                                                - [Symplectic manifolds, general](53d05.md "MISSING PAGE")
                                                - [Contact manifolds, general](53d10.md "MISSING PAGE")
                                                - [Lagrangian submanifolds; Maslov index](53d12.md "MISSING PAGE")
                                                - [Almost contact and almost symplectic manifolds](53d15.md "MISSING PAGE")
                                                - [Poisson manifolds](53d17.md "MISSING PAGE")
                                                - [Momentum maps; symplectic reduction](53d20.md "MISSING PAGE")
                                                - [Canonical transformations](53d22.md "MISSING PAGE")
                                                - [Geodesic flows](53d25.md "MISSING PAGE")
                                                - [Symplectic structures of moduli spaces](53d30.md "MISSING PAGE")
                                                - [Global theory of symplectic and contact manifolds](53d35.md "MISSING PAGE")
                                                - [Floer homology and cohomology, symplectic aspects](53d40.md "MISSING PAGE")
                                                - [Gromov-Witten invariants, quantum cohomology, Frobenius manifolds](53d45.md "MISSING PAGE")
                                                - [Geometric quantization](53d50.md "MISSING PAGE")
                                                - [Deformation quantization, star products](53d55.md "MISSING PAGE")
                                                - [None of the above, but in this section](53d99.md "MISSING PAGE")
                                                - [Applications to physics](53z05.md "MISSING PAGE")
                                    ## [General topology](54-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](54-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](54-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](54-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](54-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](54-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](54-06.md "MISSING PAGE")
                                                - [Generalities](54axx.md "MISSING PAGE")
                                                - [Topological spaces and generalizations (closure spaces, etc.)](54a05.md "MISSING PAGE")
                                                - [Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)](54a10.md "MISSING PAGE")
                                                - [Syntopogeneous structures](54a15.md "MISSING PAGE")
                                                - [Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)](54a20.md "MISSING PAGE")
                                                - [Cardinality properties (cardinal functions and inequalities, discrete subsets)](54a25.md "MISSING PAGE")
                                                - [Consistency and independence results](54a35.md "MISSING PAGE")
                                                - [Fuzzy topology](54a40.md "MISSING PAGE")
                                                - [None of the above, but in this section](54a99.md "MISSING PAGE")
                                                - [Basic constructions](54bxx.md "MISSING PAGE")
                                                - [Subspaces](54b05.md "MISSING PAGE")
                                                - [Product spaces](54b10.md "MISSING PAGE")
                                                - [Quotient spaces, decompositions](54b15.md "MISSING PAGE")
                                                - [Adjunction spaces and similar constructions](54b17.md "MISSING PAGE")
                                                - [Hyperspaces](54b20.md "MISSING PAGE")
                                                - [Categorical methods](54b30.md "MISSING PAGE")
                                                - [Spectra](54b35.md "MISSING PAGE")
                                                - [Presheaves and sheaves](54b40.md "MISSING PAGE")
                                                - [None of the above, but in this section](54b99.md "MISSING PAGE")
                                                - [Maps and general types of spaces defined by maps](54cxx.md "MISSING PAGE")
                                                - [Continuous maps](54c05.md "MISSING PAGE")
                                                - [Weak and generalized continuity](54c08.md "MISSING PAGE")
                                                - [Special maps on topological spaces (open, closed, perfect, etc.)](54c10.md "MISSING PAGE")
                                                - [Retraction](54c15.md "MISSING PAGE")
                                                - [Extension of maps](54c20.md "MISSING PAGE")
                                                - [Embedding](54c25.md "MISSING PAGE")
                                                - [Real-valued functions](54c30.md "MISSING PAGE")
                                                - [Function spaces](54c35.md "MISSING PAGE")
                                                - [Algebraic properties of function spaces](54c40.md "MISSING PAGE")
                                                - [$C$- and $C^*$-embedding](54c45.md "MISSING PAGE")
                                                - [Special sets defined by functions](54c50.md "MISSING PAGE")
                                                - [Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)](54c55.md "MISSING PAGE")
                                                - [Shape theory](54c56.md "MISSING PAGE")
                                                - [Set-valued maps](54c60.md "MISSING PAGE")
                                                - [Selections](54c65.md "MISSING PAGE")
                                                - [Entropy](54c70.md "MISSING PAGE")
                                                - [None of the above, but in this section](54c99.md "MISSING PAGE")
                                                - [Fairly general properties](54dxx.md "MISSING PAGE")
                                                - [Connected and locally connected spaces (general aspects)](54d05.md "MISSING PAGE")
                                                - [Lower separation axioms ($T_0$--$T_3$, etc.)](54d10.md "MISSING PAGE")
                                                - [Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)](54d15.md "MISSING PAGE")
                                                - [Noncompact covering properties (paracompact, Lindelöf, etc.)](54d20.md "MISSING PAGE")
                                                - [``$P$-minimal'' and ``$P$-closed'' spaces](54d25.md "MISSING PAGE")
                                                - [Compactness](54d30.md "MISSING PAGE")
                                                - [Extensions of spaces (compactifications, supercompactifications, completions, etc.)](54d35.md "MISSING PAGE")
                                                - [Remainders](54d40.md "MISSING PAGE")
                                                - [Local compactness, $sigma$-compactness](54d45.md "MISSING PAGE")
                                                - [$k$-spaces](54d50.md "MISSING PAGE")
                                                - [Sequential spaces](54d55.md "MISSING PAGE")
                                                - [Realcompactness and realcompactification](54d60.md "MISSING PAGE")
                                                - [Separability](54d65.md "MISSING PAGE")
                                                - [Base properties](54d70.md "MISSING PAGE")
                                                - [Special constructions of spaces (spaces of ultrafilters, etc.)](54d80.md "MISSING PAGE")
                                                - [None of the above, but in this section](54d99.md "MISSING PAGE")
                                                - [Spaces with richer structures](54exx.md "MISSING PAGE")
                                                - [Proximity structures and generalizations](54e05.md "MISSING PAGE")
                                                - [Uniform structures and generalizations](54e15.md "MISSING PAGE")
                                                - [Nearness spaces](54e17.md "MISSING PAGE")
                                                - [$p$-spaces, $M$-spaces, $sigma$-spaces, etc.](54e18.md "MISSING PAGE")
                                                - [Stratifiable spaces, cosmic spaces, etc.](54e20.md "MISSING PAGE")
                                                - [Semimetric spaces](54e25.md "MISSING PAGE")
                                                - [Moore spaces](54e30.md "MISSING PAGE")
                                                - [Metric spaces, metrizability](54e35.md "MISSING PAGE")
                                                - [Special maps on metric spaces](54e40.md "MISSING PAGE")
                                                - [Compact (locally compact) metric spaces](54e45.md "MISSING PAGE")
                                                - [Complete metric spaces](54e50.md "MISSING PAGE")
                                                - [Baire category, Baire spaces](54e52.md "MISSING PAGE")
                                                - [Bitopologies](54e55.md "MISSING PAGE")
                                                - [Probabilistic metric spaces](54e70.md "MISSING PAGE")
                                                - [None of the above, but in this section](54e99.md "MISSING PAGE")
                                                - [Special properties](54fxx.md "MISSING PAGE")
                                                - [Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces](54f05.md "MISSING PAGE")
                                                - [Continua and generalizations](54f15.md "MISSING PAGE")
                                                - [Higher-dimensional local connectedness](54f35.md "MISSING PAGE")
                                                - [Dimension theory](54f45.md "MISSING PAGE")
                                                - [Spaces of dimension $leq 1$; curves, dendrites](54f50.md "MISSING PAGE")
                                                - [Unicoherence, multicoherence](54f55.md "MISSING PAGE")
                                                - [Topological characterizations of particular spaces](54f65.md "MISSING PAGE")
                                                - [None of the above, but in this section](54f99.md "MISSING PAGE")
                                                - [Peculiar spaces](54gxx.md "MISSING PAGE")
                                                - [Extremally disconnected spaces, $F$-spaces, etc.](54g05.md "MISSING PAGE")
                                                - [$P$-spaces](54g10.md "MISSING PAGE")
                                                - [Scattered spaces](54g12.md "MISSING PAGE")
                                                - [Pathological spaces](54g15.md "MISSING PAGE")
                                                - [Counterexamples](54g20.md "MISSING PAGE")
                                                - [None of the above, but in this section](54g99.md "MISSING PAGE")
                                                - [Connections with other structures, applications](54hxx.md "MISSING PAGE")
                                                - [Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)](54h05.md "MISSING PAGE")
                                                - [Topological representations of algebraic systems](54h10.md "MISSING PAGE")
                                                - [Topological groups](54h11.md "MISSING PAGE")
                                                - [Topological lattices, etc.](54h12.md "MISSING PAGE")
                                                - [Topological fields, rings, etc.](54h13.md "MISSING PAGE")
                                                - [Transformation groups and semigroups](54h15.md "MISSING PAGE")
                                                - [Topological dynamics](54h20.md "MISSING PAGE")
                                                - [Fixed-point and coincidence theorems](54h25.md "MISSING PAGE")
                                                - [None of the above, but in this section](54h99.md "MISSING PAGE")
                                                - [Nonstandard topology](54j05.md "MISSING PAGE")
                                                - [Algebraic topology](55-xx.md "MISSING PAGE")
                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](55-00.md "MISSING PAGE")
                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](55-01.md "MISSING PAGE")
                                                - [Research exposition (monographs, survey articles)](55-02.md "MISSING PAGE")
                                                - [Historical (must also be assigned at least one classification number from Section 01)](55-03.md "MISSING PAGE")
                                                - [Explicit machine computation and programs (not the theory of computation or programming)](55-04.md "MISSING PAGE")
                                                - [Proceedings, conferences, collections, etc.](55-06.md "MISSING PAGE")
                                    ## [Classical topics](55mxx.md "MISSING PAGE")
                                                - [Duality](55m05.md "MISSING PAGE")
                                                - [Dimension theory](55m10.md "MISSING PAGE")
                                                - [Absolute neighborhood retracts](55m15.md "MISSING PAGE")
                                                - [Fixed points and coincidences](55m20.md "MISSING PAGE")
                                                - [Degree, winding number](55m25.md "MISSING PAGE")
                                                - [Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space](55m30.md "MISSING PAGE")
                                                - [Finite groups of transformations (including Smith theory)](55m35.md "MISSING PAGE")
                                                - [None of the above, but in this section](55m99.md "MISSING PAGE")
                                                - [Homology and cohomology theories](55nxx.md "MISSING PAGE")
                                                - [Cech types](55n05.md "MISSING PAGE")
                                                - [Steenrod-Sitnikov homologies](55n07.md "MISSING PAGE")
                                                - [Singular theory](55n10.md "MISSING PAGE")
                                                - [$K$-theory](55n15.md "MISSING PAGE")
                                                - [Generalized (extraordinary) homology and cohomology theories](55n20.md "MISSING PAGE")
                                                - [Bordism and cobordism theories, formal group laws](55n22.md "MISSING PAGE")
                                                - [Homology with local coefficients, equivariant cohomology](55n25.md "MISSING PAGE")
                                                - [Sheaf cohomology](55n30.md "MISSING PAGE")
                                                - [Intersection homology and cohomology](55n33.md "MISSING PAGE")
                                                - [Elliptic cohomology](55n34.md "MISSING PAGE")
                                                - [Other homology theories](55n35.md "MISSING PAGE")
                                                - [Axioms for homology theory and uniqueness theorems](55n40.md "MISSING PAGE")
                                                - [Products and intersections](55n45.md "MISSING PAGE")
                                                - [Equivariant homology and cohomology](55n91.md "MISSING PAGE")
                                                - [None of the above, but in this section](55n99.md "MISSING PAGE")
                                                - [Homotopy theory](55pxx.md "MISSING PAGE")
                                                - [Homotopy extension properties, cofibrations](55p05.md "MISSING PAGE")
                                                - [Homotopy equivalences](55p10.md "MISSING PAGE")
                                                - [Classification of homotopy type](55p15.md "MISSING PAGE")
                                                - [Eilenberg-Mac Lane spaces](55p20.md "MISSING PAGE")
                                                - [Spanier-Whitehead duality](55p25.md "MISSING PAGE")
                                                - [Eckmann-Hilton duality](55p30.md "MISSING PAGE")
                                                - [Loop spaces](55p35.md "MISSING PAGE")
                                                - [Suspensions](55p40.md "MISSING PAGE")
                                                - [Stable homotopy theory, spectra](55p42.md "MISSING PAGE")
                                                - [Spectra with additional structure ($E_infty$, $A_infty$, ring spectra, etc.)](55p43.md "MISSING PAGE")
                                                - [H]$-spaces and duals](55p45.md "MISSING PAGE")
                                                  [Infinite loop spaces](55p47.md "MISSING PAGE")
                                                  [Loop space machines, operads](55p48.md "MISSING PAGE")
                                                  [Shape theory](55p55.md "MISSING PAGE")
                                                  [Proper homotopy theory](55p57.md "MISSING PAGE")
                                                  [Localization and completion](55p60.md "MISSING PAGE")
                                                  [Rational homotopy theory](55p62.md "MISSING PAGE")
                                                  [Homotopy functors](55p65.md "MISSING PAGE")
                                                  [Equivariant homotopy theory](55p91.md "MISSING PAGE")
                                                  [Relations between equivariant and nonequivariant homotopy theory](55p92.md "MISSING PAGE")
                                                  [None of the above, but in this section](55p99.md "MISSING PAGE")
                                                  [Homotopy groups](55qxx.md "MISSING PAGE")
                                                  [Homotopy groups, general; sets of homotopy classes](55q05.md "MISSING PAGE")
                                                  [Shape groups](55q07.md "MISSING PAGE")
                                                  [Stable homotopy groups](55q10.md "MISSING PAGE")
                                                  [Whitehead products and generalizations](55q15.md "MISSING PAGE")
                                                  [Homotopy groups of wedges, joins, and simple spaces](55q20.md "MISSING PAGE")
                                                  [Hopf invariants](55q25.md "MISSING PAGE")
                                                  [Operations in homotopy groups](55q35.md "MISSING PAGE")
                                                  [Homotopy groups of spheres](55q40.md "MISSING PAGE")
                                                  [Stable homotopy of spheres](55q45.md "MISSING PAGE")
                                                  [$J$-morphism](55q50.md "MISSING PAGE")
                                                  [$v_n$-periodicity](55q51.md "MISSING PAGE")
                                                  [Homotopy groups of special spaces](55q52.md "MISSING PAGE")
                                                  [Cohomotopy groups](55q55.md "MISSING PAGE")
                                                  [Homotopy groups of special types](55q70.md "MISSING PAGE")
                                                  [Equivariant homotopy groups](55q91.md "MISSING PAGE")
                                                  [None of the above, but in this section](55q99.md "MISSING PAGE")
                                                  [Fiber spaces and bundles](55rxx.md "MISSING PAGE")
                                                  [Fiber spaces](55r05.md "MISSING PAGE")
                                                  [Fiber bundles](55r10.md "MISSING PAGE")
                                                  [Transfer](55r12.md "MISSING PAGE")
                                                  [Classification](55r15.md "MISSING PAGE")
                                                  [Spectral sequences and homology of fiber spaces](55r20.md "MISSING PAGE")
                                                  [Sphere bundles and vector bundles](55r25.md "MISSING PAGE")
                                                  [Classifying spaces of groups and H]$-spaces](55r35.md "MISSING PAGE")
                                                  [Maps between classifying spaces](55r37.md "MISSING PAGE")
                                                  [Homology of classifying spaces, characteristic classes](55r40.md "MISSING PAGE")
                                                  [Homology and homotopy of $B{rm O]$ and $B{rm U]$; Bott periodicity](55r45.md "MISSING PAGE")
                                                  [Stable classes of vector space bundles, $K$-theory](55r50.md "MISSING PAGE")
                                                  [Fiberings with singularities](55r55.md "MISSING PAGE")
                                                  [Microbundles and block bundles](55r60.md "MISSING PAGE")
                                                  [Generalizations of fiber spaces and bundles](55r65.md "MISSING PAGE")
                                                  [Fibrewise topology](55r70.md "MISSING PAGE")
                                                  [Discriminantal varieties, configuration spaces](55r80.md "MISSING PAGE")
                                                  [Equivariant fiber spaces and bundles](55r91.md "MISSING PAGE")
                                                  [None of the above, but in this section](55r99.md "MISSING PAGE")
                                                  [Operations and obstructions](55sxx.md "MISSING PAGE")
                                                  [Primary cohomology operations](55s05.md "MISSING PAGE")
                                                  [Steenrod algebra](55s10.md "MISSING PAGE")
                                                  [Dyer-Lashof operations](55s12.md "MISSING PAGE")
                                                  [Symmetric products, cyclic products](55s15.md "MISSING PAGE")
                                                  [Secondary and higher cohomology operations](55s20.md "MISSING PAGE")
                                                  [$K$-theory operations and generalized cohomology operations](55s25.md "MISSING PAGE")
                                                  [Massey products](55s30.md "MISSING PAGE")
                                                  [Obstruction theory](55s35.md "MISSING PAGE")
                                                  [Extension and compression of mappings](55s36.md "MISSING PAGE")
                                                  [Classification of mappings](55s37.md "MISSING PAGE")
                                                  [Sectioning fiber spaces and bundles](55s40.md "MISSING PAGE")
                                                  [Postnikov systems, $k$-invariants](55s45.md "MISSING PAGE")
                                                  [Equivariant operations and obstructions](55s91.md "MISSING PAGE")
                                                  [None of the above, but in this section](55s99.md "MISSING PAGE")
                                                  [Spectral sequences](55txx.md "MISSING PAGE")
                                                  [General](55t05.md "MISSING PAGE")
                                                  [Serre spectral sequences](55t10.md "MISSING PAGE")
                                                  [Adams spectral sequences](55t15.md "MISSING PAGE")
                                                  [Eilenberg-Moore spectral sequences](55t20.md "MISSING PAGE")
                                                  [Generalized cohomology](55t25.md "MISSING PAGE")
                                                  [None of the above, but in this section](55t99.md "MISSING PAGE")
                                                  [Applied homological algebra and category theory](55uxx.md "MISSING PAGE")
                                                  [Abstract complexes](55u05.md "MISSING PAGE")
                                                  [Simplicial sets and complexes](55u10.md "MISSING PAGE")
                                                  [Chain complexes](55u15.md "MISSING PAGE")
                                                  [Universal coefficient theorems, Bockstein operator](55u20.md "MISSING PAGE")
                                                  [Homology of a product, Künneth formula](55u25.md "MISSING PAGE")
                                                  [Duality](55u30.md "MISSING PAGE")
                                                  [Abstract and axiomatic homotopy theory](55u35.md "MISSING PAGE")
                                                  [Topological categories, foundations of homotopy theory](55u40.md "MISSING PAGE")
                                                  [None of the above, but in this section](55u99.md "MISSING PAGE")
                                                  ## [Manifolds and cell complexes](57-xx.md "MISSING PAGE")
                                                                - [General reference works (handbooks, dictionaries, bibliographies, etc.)](57-00.md "MISSING PAGE")
                                                                - [Instructional exposition (textbooks, tutorial papers, etc.)](57-01.md "MISSING PAGE")
                                                                - [Research exposition (monographs, survey articles)](57-02.md "MISSING PAGE")
                                                                - [Historical (must also be assigned at least one classification number from Section 01)](57-03.md "MISSING PAGE")
                                                                - [Explicit machine computation and programs (not the theory of computation or programming)](57-04.md "MISSING PAGE")
                                                                - [Proceedings, conferences, collections, etc.](57-06.md "MISSING PAGE")
                                                                - [Low-dimensional topology](57mxx.md "MISSING PAGE")
                                                                - [Fundamental group, presentations, free differential calculus](57m05.md "MISSING PAGE")
                                                                - [Topological methods in group theory](57m07.md "MISSING PAGE")
                                                                - [Covering spaces](57m10.md "MISSING PAGE")
                                                                - [Special coverings, e.g. branched](57m12.md "MISSING PAGE")
                                                                - [Relations with graph theory](57m15.md "MISSING PAGE")
                                                                - [Two-dimensional complexes](57m20.md "MISSING PAGE")
                                                                - [Knots and links in $S^3$](57m25.md "MISSING PAGE")
                                                                - [Invariants of knots and 3-manifolds](57m27.md "MISSING PAGE")
                                                                - [Wild knots and surfaces, etc., wild embeddings](57m30.md "MISSING PAGE")
                                                                - [Dehn's lemma, sphere theorem, loop theorem, asphericity](57m35.md "MISSING PAGE")
                                                                - [Characterizations of $E^3$ and $S^3$ (Poincaré conjecture)](57m40.md "MISSING PAGE")
                                                                - [Geometric structures on low-dimensional manifolds](57m50.md "MISSING PAGE")
                                                                - [Group actions in low dimensions](57m60.md "MISSING PAGE")
                                                                - [None of the above, but in this section](57m99.md "MISSING PAGE")
                                                                - [Topological manifolds](57nxx.md "MISSING PAGE")
                                                                - [Topology of $E^2$, $2$-manifolds](57n05.md "MISSING PAGE")
                                                                - [Topology of general $3$-manifolds](57n10.md "MISSING PAGE")
                                                                - [Topology of $E^3$ and $S^3$](57n12.md "MISSING PAGE")
                                                                - [Topology of $E^4$, $4$-manifolds](57n13.md "MISSING PAGE")
                                                                - [Topology of $E^n$, $n$-manifolds ($4 &lt; n &lt; infty$)](57n15.md "MISSING PAGE")
                                                                - [Geometric structures on manifolds](57n16.md "MISSING PAGE")
                                                                - [Topology of topological vector spaces](57n17.md "MISSING PAGE")
                                                                - [Topology of infinite-dimensional manifolds](57n20.md "MISSING PAGE")
                                                                - [Shapes](57n25.md "MISSING PAGE")
                                                                - [Engulfing](57n30.md "MISSING PAGE")
                                                                - [Embeddings and immersions](57n35.md "MISSING PAGE")
                                                                - [Isotopy and pseudo-isotopy](57n37.md "MISSING PAGE")
                                                                - [Neighborhoods of submanifolds](57n40.md "MISSING PAGE")
                                                                - [Flatness and tameness](57n45.md "MISSING PAGE")
                                                                - [$Sn-1]subset E^n$, Schoenflies problem](57n50.md "MISSING PAGE")
                                                                  [Microbundles and block bundles](57n55.md "MISSING PAGE")
                                                                  [Cellularity](57n60.md "MISSING PAGE")
                                                                  [Algebraic topology of manifolds](57n65.md "MISSING PAGE")
                                                                  [Cobordism and concordance](57n70.md "MISSING PAGE")
                                                                  [General position and transversality](57n75.md "MISSING PAGE")
                                                                  [Stratifications](57n80.md "MISSING PAGE")
                                                                  [None of the above, but in this section](57n99.md "MISSING PAGE")
                                                                  [Generalized manifolds](57pxx.md "MISSING PAGE")
                                                                  [Local properties of generalized manifolds](57p05.md "MISSING PAGE")
                                                                  [Poincaré duality spaces](57p10.md "MISSING PAGE")
                                                                  [None of the above, but in this section](57p99.md "MISSING PAGE")
                                                                  [PL-topology](57qxx.md "MISSING PAGE")
                                                                  [General topology of complexes](57q05.md "MISSING PAGE")
                                                                  [Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.](57q10.md "MISSING PAGE")
                                                                  [Wall finiteness obstruction for CW-complexes](57q12.md "MISSING PAGE")
                                                                  [Triangulating manifolds](57q15.md "MISSING PAGE")
                                                                  [Cobordism](57q20.md "MISSING PAGE")
                                                                  [Comparison of PL-structures: classification, Hauptvermutung](57q25.md "MISSING PAGE")
                                                                  [Engulfing](57q30.md "MISSING PAGE")
                                                                  [Embeddings and immersions](57q35.md "MISSING PAGE")
                                                                  [Isotopy](57q37.md "MISSING PAGE")
                                                                  [Regular neighborhoods](57q40.md "MISSING PAGE")
                                                                  [Knots and links (in high dimensions)](57q45.md "MISSING PAGE")
                                                                  [Microbundles and block bundles](57q50.md "MISSING PAGE")
                                                                  [Approximations](57q55.md "MISSING PAGE")
                                                                  [Cobordism and concordance](57q60.md "MISSING PAGE")
                                                                  [General position and transversality](57q65.md "MISSING PAGE")
                                                                  [Equivariant PL-topology](57q91.md "MISSING PAGE")
                                                                  [None of the above, but in this section](57q99.md "MISSING PAGE")
                                                                  [Differential topology](57rxx.md "MISSING PAGE")
                                                                  [Triangulating](57r05.md "MISSING PAGE")
                                                                  [Smoothing](57r10.md "MISSING PAGE")
                                                                  [Smooth approximations](57r12.md "MISSING PAGE")
                                                                  [Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)](57r15.md "MISSING PAGE")
                                                                  [Symplectic and contact topology](57r17.md "MISSING PAGE")
                                                                  [Algebraic topology on manifolds](57r19.md "MISSING PAGE")
                                                                  [Characteristic classes and numbers](57r20.md "MISSING PAGE")
                                                                  [Topology of vector bundles and fiber bundles](57r22.md "MISSING PAGE")
                                                                  [Vector fields, frame fields](57r25.md "MISSING PAGE")
                                                                  [Controllability of vector fields on $C^infty$ and real-analytic manifolds](57r27.md "MISSING PAGE")
                                                                  [Foliations; geometric theory](57r30.md "MISSING PAGE")
                                                                  [Classifying spaces for foliations; Gelfand-Fuks cohomology](57r32.md "MISSING PAGE")
                                                                  [Differentiable mappings](57r35.md "MISSING PAGE")
                                                                  [Embeddings](57r40.md "MISSING PAGE")
                                                                  [Immersions](57r42.md "MISSING PAGE")
                                                                  [Singularities of differentiable mappings](57r45.md "MISSING PAGE")
                                                                  [Diffeomorphisms](57r50.md "MISSING PAGE")
                                                                  [Isotopy](57r52.md "MISSING PAGE")
                                                                  [Differentiable structures](57r55.md "MISSING PAGE")
                                                                  [Topological quantum field theories](57r56.md "MISSING PAGE")
                                                                  [Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants](57r57.md "MISSING PAGE")
                                                                  [Floer homology](57r58.md "MISSING PAGE")
                                                                  [Homotopy spheres, Poincaré conjecture](57r60.md "MISSING PAGE")
                                                                  [Surgery and handlebodies](57r65.md "MISSING PAGE")
                                                                  [Surgery obstructions, Wall groups](57r67.md "MISSING PAGE")
                                                                  [Critical points and critical submanifolds](57r70.md "MISSING PAGE")
                                                                  [O- and SO-cobordism](57r75.md "MISSING PAGE")
                                                                  [Complex cobordism (U- and SU-cobordism)](57r77.md "MISSING PAGE")
                                                                  [$h$- and $s$-cobordism](57r80.md "MISSING PAGE")
                                                                  [Equivariant cobordism](57r85.md "MISSING PAGE")
                                                                  [Other types of cobordism](57r90.md "MISSING PAGE")
                                                                  [Equivariant algebraic topology of manifolds](57r91.md "MISSING PAGE")
                                                                  [Realizing cycles by submanifolds](57r95.md "MISSING PAGE")
                                                                  [None of the above, but in this section](57r99.md "MISSING PAGE")
                                                                  [Topological transformation groups](57sxx.md "MISSING PAGE")
                                                                  [Topological properties of groups of homeomorphisms or diffeomorphisms](57s05.md "MISSING PAGE")
                                                                  [Compact groups of homeomorphisms](57s10.md "MISSING PAGE")
                                                                  [Compact Lie groups of differentiable transformations](57s15.md "MISSING PAGE")
                                                                  [Finite transformation groups](57s17.md "MISSING PAGE")
                                                                  [Noncompact Lie groups of transformations](57s20.md "MISSING PAGE")
                                                                  [Groups acting on specific manifolds](57s25.md "MISSING PAGE")
                                                                  [Discontinuous groups of transformations](57s30.md "MISSING PAGE")
                                                                  [None of the above, but in this section](57s99.md "MISSING PAGE")
                                                                  [Homology and homotopy of topological groups and related structures](57txx.md "MISSING PAGE")
                                                                  [Hopf algebras](57t05.md "MISSING PAGE")
                                                                  [Homology and cohomology of Lie groups](57t10.md "MISSING PAGE")
                                                                  [Homology and cohomology of homogeneous spaces of Lie groups](57t15.md "MISSING PAGE")
                                                                  [Homotopy groups of topological groups and homogeneous spaces](57t20.md "MISSING PAGE")
                                                                  [Homology and cohomology of H]$-spaces](57t25.md "MISSING PAGE")
                                                                  [Bar and cobar constructions](57t30.md "MISSING PAGE")
                                                                  [Applications of Eilenberg-Moore spectral sequences](57t35.md "MISSING PAGE")
                                                                  [None of the above, but in this section](57t99.md "MISSING PAGE")
                                                                  ## [Global analysis, analysis on manifolds](58-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](58-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](58-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](58-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](58-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](58-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](58-06.md "MISSING PAGE")
                                                                                  - [General theory of differentiable manifolds](58axx.md "MISSING PAGE")
                                                                                  - [Topos-theoretic approach to differentiable manifolds](58a03.md "MISSING PAGE")
                                                                                  - [Differentiable manifolds, foundations](58a05.md "MISSING PAGE")
                                                                                  - [Real-analytic and Nash manifolds](58a07.md "MISSING PAGE")
                                                                                  - [Differential forms](58a10.md "MISSING PAGE")
                                                                                  - [de Rham theory](58a12.md "MISSING PAGE")
                                                                                  - [Hodge theory](58a14.md "MISSING PAGE")
                                                                                  - [Exterior differential systems (Cartan theory)](58a15.md "MISSING PAGE")
                                                                                  - [Pfaffian systems](58a17.md "MISSING PAGE")
                                                                                  - [Jets](58a20.md "MISSING PAGE")
                                                                                  - [Currents](58a25.md "MISSING PAGE")
                                                                                  - [Vector distributions (subbundles of the tangent bundles)](58a30.md "MISSING PAGE")
                                                                                  - [Natural bundles](58a32.md "MISSING PAGE")
                                                                                  - [Stratified sets](58a35.md "MISSING PAGE")
                                                                                  - [Differential spaces](58a40.md "MISSING PAGE")
                                                                                  - [Supermanifolds and graded manifolds](58a50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58a99.md "MISSING PAGE")
                                                                                  - [Infinite-dimensional manifolds](58bxx.md "MISSING PAGE")
                                                                                  - [Homotopy and topological questions](58b05.md "MISSING PAGE")
                                                                                  - [Differentiability questions](58b10.md "MISSING PAGE")
                                                                                  - [Questions of holomorphy](58b12.md "MISSING PAGE")
                                                                                  - [Fredholm structures](58b15.md "MISSING PAGE")
                                                                                  - [Riemannian, Finsler and other geometric structures](58b20.md "MISSING PAGE")
                                                                                  - [Group structures and generalizations on infinite-dimensional manifolds](58b25.md "MISSING PAGE")
                                                                                  - [Geometry of quantum groups](58b32.md "MISSING PAGE")
                                                                                  - [Noncommutative geometry (à la Connes)](58b34.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58b99.md "MISSING PAGE")
                                                                                  - [Calculus on manifolds; nonlinear operators](58cxx.md "MISSING PAGE")
                                                                                  - [Real-valued functions](58c05.md "MISSING PAGE")
                                                                                  - [Set valued and function-space valued mappings](58c06.md "MISSING PAGE")
                                                                                  - [Continuity properties of mappings](58c07.md "MISSING PAGE")
                                                                                  - [Holomorphic maps](58c10.md "MISSING PAGE")
                                                                                  - [Implicit function theorems; global Newton methods](58c15.md "MISSING PAGE")
                                                                                  - [Differentiation theory (Gateaux, Fréchet, etc.)](58c20.md "MISSING PAGE")
                                                                                  - [Differentiable maps](58c25.md "MISSING PAGE")
                                                                                  - [Fixed point theorems on manifolds](58c30.md "MISSING PAGE")
                                                                                  - [Integration on manifolds; measures on manifolds](58c35.md "MISSING PAGE")
                                                                                  - [Spectral theory; eigenvalue problems](58c40.md "MISSING PAGE")
                                                                                  - [Analysis on supermanifolds or graded manifolds](58c50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58c99.md "MISSING PAGE")
                                                                                  - [Spaces and manifolds of mappings (including nonlinear versions of 46Exx)](58dxx.md "MISSING PAGE")
                                                                                  - [Groups of diffeomorphisms and homeomorphisms as manifolds](58d05.md "MISSING PAGE")
                                                                                  - [Groups and semigroups of nonlinear operators](58d07.md "MISSING PAGE")
                                                                                  - [Spaces of imbeddings and immersions](58d10.md "MISSING PAGE")
                                                                                  - [Manifolds of mappings](58d15.md "MISSING PAGE")
                                                                                  - [Manifolds of metrics (esp. Riemannian)](58d17.md "MISSING PAGE")
                                                                                  - [Group actions and symmetry properties](58d19.md "MISSING PAGE")
                                                                                  - [Measures (Gaussian, cylindrical, etc.) on manifolds of maps](58d20.md "MISSING PAGE")
                                                                                  - [Equations in function spaces; evolution equations](58d25.md "MISSING PAGE")
                                                                                  - [Moduli problems for differential geometric structures](58d27.md "MISSING PAGE")
                                                                                  - [Moduli problems for topological structures](58d29.md "MISSING PAGE")
                                                                                  - [Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)](58d30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58d99.md "MISSING PAGE")
                                                                                  - [Variational problems in infinite-dimensional spaces](58exx.md "MISSING PAGE")
                                                                                  - [Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)](58e05.md "MISSING PAGE")
                                                                                  - [Abstract bifurcation theory](58e07.md "MISSING PAGE")
                                                                                  - [Group-invariant bifurcation theory](58e09.md "MISSING PAGE")
                                                                                  - [Applications to the theory of geodesics (problems in one independent variable)](58e10.md "MISSING PAGE")
                                                                                  - [Critical metrics](58e11.md "MISSING PAGE")
                                                                                  - [Applications to minimal surfaces (problems in two independent variables)](58e12.md "MISSING PAGE")
                                                                                  - [Application to extremal problems in several variables; Yang-Mills functionals, etc.](58e15.md "MISSING PAGE")
                                                                                  - [Pareto optimality, etc., applications to economics](58e17.md "MISSING PAGE")
                                                                                  - [Harmonic maps, etc.](58e20.md "MISSING PAGE")
                                                                                  - [Applications to control theory](58e25.md "MISSING PAGE")
                                                                                  - [Variational principles](58e30.md "MISSING PAGE")
                                                                                  - [Variational inequalities (global problems)](58e35.md "MISSING PAGE")
                                                                                  - [Group actions](58e40.md "MISSING PAGE")
                                                                                  - [Applications](58e50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58e99.md "MISSING PAGE")
                                                                                  - [Pseudogroups, differentiable groupoids and general structures on manifolds](58hxx.md "MISSING PAGE")
                                                                                  - [Pseudogroups and differentiable groupoids](58h05.md "MISSING PAGE")
                                                                                  - [Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)](58h10.md "MISSING PAGE")
                                                                                  - [Deformations of structures](58h15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58h99.md "MISSING PAGE")
                                                                                  - [Partial differential equations on manifolds; differential operators](58jxx.md "MISSING PAGE")
                                                                                  - [Elliptic equations on manifolds, general theory](58j05.md "MISSING PAGE")
                                                                                  - [Differential complexes; elliptic complexes](58j10.md "MISSING PAGE")
                                                                                  - [Relations with hyperfunctions](58j15.md "MISSING PAGE")
                                                                                  - [Index theory and related fixed point theorems](58j20.md "MISSING PAGE")
                                                                                  - [Exotic index theories](58j22.md "MISSING PAGE")
                                                                                  - [Elliptic genera](58j26.md "MISSING PAGE")
                                                                                  - [Eta-invariants, Chern-Simons invariants](58j28.md "MISSING PAGE")
                                                                                  - [Spectral flows](58j30.md "MISSING PAGE")
                                                                                  - [Boundary value problems on manifolds](58j32.md "MISSING PAGE")
                                                                                  - [Heat and other parabolic equation methods](58j35.md "MISSING PAGE")
                                                                                  - [Perturbations; asymptotics](58j37.md "MISSING PAGE")
                                                                                  - [Pseudodifferential and Fourier integral operators on manifolds](58j40.md "MISSING PAGE")
                                                                                  - [Noncommutative global analysis, noncommutative residues](58j42.md "MISSING PAGE")
                                                                                  - [Hyperbolic equations](58j45.md "MISSING PAGE")
                                                                                  - [Propagation of singularities; initial value problems](58j47.md "MISSING PAGE")
                                                                                  - [Spectral problems; spectral geometry; scattering theory](58j50.md "MISSING PAGE")
                                                                                  - [Determinants and determinant bundles, analytic torsion](58j52.md "MISSING PAGE")
                                                                                  - [Isospectrality](58j53.md "MISSING PAGE")
                                                                                  - [Bifurcation](58j55.md "MISSING PAGE")
                                                                                  - [Relations with special manifold structures (Riemannian, Finsler, etc.)](58j60.md "MISSING PAGE")
                                                                                  - [Diffusion processes and stochastic analysis on manifolds](58j65.md "MISSING PAGE")
                                                                                  - [Invariance and symmetry properties](58j70.md "MISSING PAGE")
                                                                                  - [Correspondences and other transformation methods (e.g. Lie-Bäcklund)](58j72.md "MISSING PAGE")
                                                                                  - [Applications](58j90.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58j99.md "MISSING PAGE")
                                                                                  - [Theory of singularities and catastrophe theory](58kxx.md "MISSING PAGE")
                                                                                  - [Critical points of functions and mappings](58k05.md "MISSING PAGE")
                                                                                  - [Monodromy](58k10.md "MISSING PAGE")
                                                                                  - [Topological properties of mappings](58k15.md "MISSING PAGE")
                                                                                  - [Algebraic and analytic properties of mappings](58k20.md "MISSING PAGE")
                                                                                  - [Stability](58k25.md "MISSING PAGE")
                                                                                  - [Global theory](58k30.md "MISSING PAGE")
                                                                                  - [Catastrophe theory](58k35.md "MISSING PAGE")
                                                                                  - [Classification; finite determinacy of map germs](58k40.md "MISSING PAGE")
                                                                                  - [Singularities of vector fields, topological aspects](58k45.md "MISSING PAGE")
                                                                                  - [Normal forms](58k50.md "MISSING PAGE")
                                                                                  - [Asymptotic behavior](58k55.md "MISSING PAGE")
                                                                                  - [Deformation of singularities](58k60.md "MISSING PAGE")
                                                                                  - [Topological invariants](58k65.md "MISSING PAGE")
                                                                                  - [Symmetries, equivariance](58k70.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](58k99.md "MISSING PAGE")
                                                                                  - [Applications to physics](58z05.md "MISSING PAGE")
                                                                  ## [Probability theory and stochastic processes](60-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](60-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](60-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](60-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](60-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](60-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](60-06.md "MISSING PAGE")
                                                                                  - [Computational methods (not classified at a more specific level)](60-08.md "MISSING PAGE")
                                                                                  - [Foundations of probability theory](60axx.md "MISSING PAGE")
                                                                                  - [Axioms; other general questions](60a05.md "MISSING PAGE")
                                                                                  - [Probabilistic measure theory](60a10.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60a99.md "MISSING PAGE")
                                                                                  - [Probability theory on algebraic and topological structures](60bxx.md "MISSING PAGE")
                                                                                  - [Probability measures on topological spaces](60b05.md "MISSING PAGE")
                                                                                  - [Convergence of probability measures](60b10.md "MISSING PAGE")
                                                                                  - [Probability theory on linear topological spaces](60b11.md "MISSING PAGE")
                                                                                  - [Limit theorems for vector-valued random variables (infinite-dimensional case)](60b12.md "MISSING PAGE")
                                                                                  - [Probability measures on groups, Fourier transforms, factorization](60b15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60b99.md "MISSING PAGE")
                                                                                  - [Combinatorial probability](60c05.md "MISSING PAGE")
                                                                                  - [Geometric probability, stochastic geometry, random sets](60d05.md "MISSING PAGE")
                                                                                  - [Distribution theory](60exx.md "MISSING PAGE")
                                                                                  - [Distributions: general theory](60e05.md "MISSING PAGE")
                                                                                  - [Infinitely divisible distributions; stable distributions](60e07.md "MISSING PAGE")
                                                                                  - [Characteristic functions; other transforms](60e10.md "MISSING PAGE")
                                                                                  - [Inequalities; stochastic orderings](60e15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60e99.md "MISSING PAGE")
                                                                                  - [Limit theorems](60fxx.md "MISSING PAGE")
                                                                                  - [Central limit and other weak theorems](60f05.md "MISSING PAGE")
                                                                                  - [Large deviations](60f10.md "MISSING PAGE")
                                                                                  - [Strong theorems](60f15.md "MISSING PAGE")
                                                                                  - [Functional limit theorems; invariance principles](60f17.md "MISSING PAGE")
                                                                                  - [Zero-one laws](60f20.md "MISSING PAGE")
                                                                                  - [$L^p$-limit theorems](60f25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60f99.md "MISSING PAGE")
                                                                                  - [Stochastic processes](60gxx.md "MISSING PAGE")
                                                                                  - [Foundations of stochastic processes](60g05.md "MISSING PAGE")
                                                                                  - [General theory of processes](60g07.md "MISSING PAGE")
                                                                                  - [Exchangeability](60g09.md "MISSING PAGE")
                                                                                  - [Stationary processes](60g10.md "MISSING PAGE")
                                                                                  - [General second-order processes](60g12.md "MISSING PAGE")
                                                                                  - [Gaussian processes](60g15.md "MISSING PAGE")
                                                                                  - [Sample path properties](60g17.md "MISSING PAGE")
                                                                                  - [Self-similar processes](60g18.md "MISSING PAGE")
                                                                                  - [Generalized stochastic processes](60g20.md "MISSING PAGE")
                                                                                  - [Prediction theory](60g25.md "MISSING PAGE")
                                                                                  - [Continuity and singularity of induced measures](60g30.md "MISSING PAGE")
                                                                                  - [Applications (signal detection, filtering, etc.)](60g35.md "MISSING PAGE")
                                                                                  - [Stopping times; optimal stopping problems; gambling theory](60g40.md "MISSING PAGE")
                                                                                  - [Martingales with discrete parameter](60g42.md "MISSING PAGE")
                                                                                  - [Martingales with continuous parameter](60g44.md "MISSING PAGE")
                                                                                  - [Martingales and classical analysis](60g46.md "MISSING PAGE")
                                                                                  - [Generalizations of martingales](60g48.md "MISSING PAGE")
                                                                                  - [Sums of independent random variables; random walks](60g50.md "MISSING PAGE")
                                                                                  - [Processes with independent increments](60g51.md "MISSING PAGE")
                                                                                  - [Stable processes](60g52.md "MISSING PAGE")
                                                                                  - [Point processes](60g55.md "MISSING PAGE")
                                                                                  - [Random measures](60g57.md "MISSING PAGE")
                                                                                  - [Random fields](60g60.md "MISSING PAGE")
                                                                                  - [Extreme value theory; extremal processes](60g70.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60g99.md "MISSING PAGE")
                                                                                  - [Stochastic analysis](60hxx.md "MISSING PAGE")
                                                                                  - [Stochastic integrals](60h05.md "MISSING PAGE")
                                                                                  - [Stochastic calculus of variations and the Malliavin calculus](60h07.md "MISSING PAGE")
                                                                                  - [Stochastic ordinary differential equations](60h10.md "MISSING PAGE")
                                                                                  - [Stochastic partial differential equations](60h15.md "MISSING PAGE")
                                                                                  - [Stochastic integral equations](60h20.md "MISSING PAGE")
                                                                                  - [Random operators and equations](60h25.md "MISSING PAGE")
                                                                                  - [Applications of stochastic analysis (to PDE, etc.)](60h30.md "MISSING PAGE")
                                                                                  - [Computational methods for stochastic equations](60h35.md "MISSING PAGE")
                                                                                  - [White noise theory](60h40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60h99.md "MISSING PAGE")
                                                                                  - [Markov processes](60jxx.md "MISSING PAGE")
                                                                                  - [Markov processes with discrete parameter](60j05.md "MISSING PAGE")
                                                                                  - [Markov chains with discrete parameter](60j10.md "MISSING PAGE")
                                                                                  - [Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.)](60j20.md "MISSING PAGE")
                                                                                  - [Computational methods in Markov chains](60j22.md "MISSING PAGE")
                                                                                  - [Markov processes with continuous parameter](60j25.md "MISSING PAGE")
                                                                                  - [Markov chains with continuous parameter](60j27.md "MISSING PAGE")
                                                                                  - [Transition functions, generators and resolvents](60j35.md "MISSING PAGE")
                                                                                  - [Right processes](60j40.md "MISSING PAGE")
                                                                                  - [Probabilistic potential theory](60j45.md "MISSING PAGE")
                                                                                  - [Boundary theory](60j50.md "MISSING PAGE")
                                                                                  - [Local time and additive functionals](60j55.md "MISSING PAGE")
                                                                                  - [Multiplicative functionals](60j57.md "MISSING PAGE")
                                                                                  - [Diffusion processes](60j60.md "MISSING PAGE")
                                                                                  - [Brownian motion](60j65.md "MISSING PAGE")
                                                                                  - [Applications of diffusion theory (population genetics, absorption problems, etc.)](60j70.md "MISSING PAGE")
                                                                                  - [Jump processes](60j75.md "MISSING PAGE")
                                                                                  - [Branching processes (Galton-Watson, birth-and-death, etc.)](60j80.md "MISSING PAGE")
                                                                                  - [Applications of branching processes](60j85.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60j99.md "MISSING PAGE")
                                                                                  - [Special processes](60kxx.md "MISSING PAGE")
                                                                                  - [Renewal theory](60k05.md "MISSING PAGE")
                                                                                  - [Applications (reliability, demand theory, etc.)](60k10.md "MISSING PAGE")
                                                                                  - [Markov renewal processes, semi-Markov processes](60k15.md "MISSING PAGE")
                                                                                  - [Applications of Markov renewal processes (reliability, queueing networks, etc.)](60k20.md "MISSING PAGE")
                                                                                  - [Queueing theory](60k25.md "MISSING PAGE")
                                                                                  - [Applications (congestion, allocation, storage, traffic, etc.)](60k30.md "MISSING PAGE")
                                                                                  - [Interacting random processes; statistical mechanics type models; percolation theory](60k35.md "MISSING PAGE")
                                                                                  - [Processes in random environments](60k37.md "MISSING PAGE")
                                                                                  - [Other physical applications of random processes](60k40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](60k99.md "MISSING PAGE")
                                                                  ## [Statistics](62-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](62-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](62-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](62-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](62-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](62-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](62-06.md "MISSING PAGE")
                                                                                  - [Data analysis](62-07.md "MISSING PAGE")
                                                                                  - [Graphical methods](62-09.md "MISSING PAGE")
                                                                                  - [Foundational and philosophical topics](62a01.md "MISSING PAGE")
                                                                                  - [Sufficiency and information](62bxx.md "MISSING PAGE")
                                                                                  - [Sufficient statistics and fields](62b05.md "MISSING PAGE")
                                                                                  - [Information-theoretic topics](62b10.md "MISSING PAGE")
                                                                                  - [Theory of statistical experiments](62b15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62b99.md "MISSING PAGE")
                                                                                  - [Decision theory](62cxx.md "MISSING PAGE")
                                                                                  - [General considerations](62c05.md "MISSING PAGE")
                                                                                  - [Complete class results](62c07.md "MISSING PAGE")
                                                                                  - [Bayesian problems; characterization of Bayes procedures](62c10.md "MISSING PAGE")
                                                                                  - [Empirical decision procedures; empirical Bayes procedures](62c12.md "MISSING PAGE")
                                                                                  - [Admissibility](62c15.md "MISSING PAGE")
                                                                                  - [Minimax procedures](62c20.md "MISSING PAGE")
                                                                                  - [Compound decision problems](62c25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62c99.md "MISSING PAGE")
                                                                                  - [Sampling theory, sample surveys](62d05.md "MISSING PAGE")
                                                                                  - [Distribution theory](62exx.md "MISSING PAGE")
                                                                                  - [Characterization and structure theory](62e10.md "MISSING PAGE")
                                                                                  - [Exact distribution theory](62e15.md "MISSING PAGE")
                                                                                  - [Approximations to distributions (nonasymptotic)](62e17.md "MISSING PAGE")
                                                                                  - [Asymptotic distribution theory](62e20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62e99.md "MISSING PAGE")
                                                                                  - [Parametric inference](62fxx.md "MISSING PAGE")
                                                                                  - [Hypothesis testing](62f03.md "MISSING PAGE")
                                                                                  - [Asymptotic properties of tests](62f05.md "MISSING PAGE")
                                                                                  - [Ranking and selection](62f07.md "MISSING PAGE")
                                                                                  - [Point estimation](62f10.md "MISSING PAGE")
                                                                                  - [Asymptotic properties of estimators](62f12.md "MISSING PAGE")
                                                                                  - [Bayesian inference](62f15.md "MISSING PAGE")
                                                                                  - [Tolerance and confidence regions](62f25.md "MISSING PAGE")
                                                                                  - [Inference under constraints](62f30.md "MISSING PAGE")
                                                                                  - [Robustness and adaptive procedures](62f35.md "MISSING PAGE")
                                                                                  - [Bootstrap, jackknife and other resampling methods](62f40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62f99.md "MISSING PAGE")
                                                                                  - [Nonparametric inference](62gxx.md "MISSING PAGE")
                                                                                  - [Estimation](62g05.md "MISSING PAGE")
                                                                                  - [Density estimation](62g07.md "MISSING PAGE")
                                                                                  - [Nonparametric regression](62g08.md "MISSING PAGE")
                                                                                  - [Resampling methods](62g09.md "MISSING PAGE")
                                                                                  - [Hypothesis testing](62g10.md "MISSING PAGE")
                                                                                  - [Tolerance and confidence regions](62g15.md "MISSING PAGE")
                                                                                  - [Asymptotic properties](62g20.md "MISSING PAGE")
                                                                                  - [Order statistics; empirical distribution functions](62g30.md "MISSING PAGE")
                                                                                  - [Statistics of extreme values; tail inference](62g32.md "MISSING PAGE")
                                                                                  - [Robustness](62g35.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62g99.md "MISSING PAGE")
                                                                                  - [Multivariate analysis](62hxx.md "MISSING PAGE")
                                                                                  - [Characterization and structure theory](62h05.md "MISSING PAGE")
                                                                                  - [Distribution of statistics](62h10.md "MISSING PAGE")
                                                                                  - [Directional data; spatial statistics](62h11.md "MISSING PAGE")
                                                                                  - [Estimation](62h12.md "MISSING PAGE")
                                                                                  - [Hypothesis testing](62h15.md "MISSING PAGE")
                                                                                  - [Contingency tables](62h17.md "MISSING PAGE")
                                                                                  - [Measures of association (correlation, canonical correlation, etc.)](62h20.md "MISSING PAGE")
                                                                                  - [Factor analysis and principal components; correspondence analysis](62h25.md "MISSING PAGE")
                                                                                  - [Classification and discrimination; cluster analysis](62h30.md "MISSING PAGE")
                                                                                  - [Image analysis](62h35.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62h99.md "MISSING PAGE")
                                                                                  - [Linear inference, regression](62jxx.md "MISSING PAGE")
                                                                                  - [General nonlinear regression](62j02.md "MISSING PAGE")
                                                                                  - [Linear regression](62j05.md "MISSING PAGE")
                                                                                  - [Ridge regression; shrinkage estimators](62j07.md "MISSING PAGE")
                                                                                  - [Analysis of variance and covariance](62j10.md "MISSING PAGE")
                                                                                  - [Generalized linear models](62j12.md "MISSING PAGE")
                                                                                  - [Paired and multiple comparisons](62j15.md "MISSING PAGE")
                                                                                  - [Diagnostics](62j20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62j99.md "MISSING PAGE")
                                                                                  - [Design of experiments](62kxx.md "MISSING PAGE")
                                                                                  - [Optimal designs](62k05.md "MISSING PAGE")
                                                                                  - [Block designs](62k10.md "MISSING PAGE")
                                                                                  - [Factorial designs](62k15.md "MISSING PAGE")
                                                                                  - [Response surface designs](62k20.md "MISSING PAGE")
                                                                                  - [Robust parameter designs](62k25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62k99.md "MISSING PAGE")
                                                                                  - [Sequential methods](62lxx.md "MISSING PAGE")
                                                                                  - [Sequential design](62l05.md "MISSING PAGE")
                                                                                  - [Sequential analysis](62l10.md "MISSING PAGE")
                                                                                  - [Sequential estimation](62l12.md "MISSING PAGE")
                                                                                  - [Optimal stopping](62l15.md "MISSING PAGE")
                                                                                  - [Stochastic approximation](62l20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62l99.md "MISSING PAGE")
                                                                                  - [Inference from stochastic processes](62mxx.md "MISSING PAGE")
                                                                                  - [Markov processes: hypothesis testing](62m02.md "MISSING PAGE")
                                                                                  - [Markov processes: estimation](62m05.md "MISSING PAGE")
                                                                                  - [Non-Markovian processes: hypothesis testing](62m07.md "MISSING PAGE")
                                                                                  - [Non-Markovian processes: estimation](62m09.md "MISSING PAGE")
                                                                                  - [Time series, auto-correlation, regression, etc.](62m10.md "MISSING PAGE")
                                                                                  - [Spectral analysis](62m15.md "MISSING PAGE")
                                                                                  - [Prediction; filtering](62m20.md "MISSING PAGE")
                                                                                  - [Spatial processes](62m30.md "MISSING PAGE")
                                                                                  - [Random fields; image analysis](62m40.md "MISSING PAGE")
                                                                                  - [Neural nets and related approaches](62m45.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62m99.md "MISSING PAGE")
                                                                                  - [Survival analysis and censored data](62nxx.md "MISSING PAGE")
                                                                                  - [Censored data models](62n01.md "MISSING PAGE")
                                                                                  - [Estimation](62n02.md "MISSING PAGE")
                                                                                  - [Testing](62n03.md "MISSING PAGE")
                                                                                  - [Reliability and life testing](62n05.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62n99.md "MISSING PAGE")
                                                                                  - [Applications](62pxx.md "MISSING PAGE")
                                                                                  - [Applications to actuarial sciences and financial mathematics](62p05.md "MISSING PAGE")
                                                                                  - [Applications to biology and medical sciences](62p10.md "MISSING PAGE")
                                                                                  - [Applications to environmental and related topics](62p12.md "MISSING PAGE")
                                                                                  - [Applications to psychology](62p15.md "MISSING PAGE")
                                                                                  - [Applications to economics](62p20.md "MISSING PAGE")
                                                                                  - [Applications to social sciences](62p25.md "MISSING PAGE")
                                                                                  - [Applications in engineering and industry](62p30.md "MISSING PAGE")
                                                                                  - [Applications to physics](62p35.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](62p99.md "MISSING PAGE")
                                                                                  - [Statistical tables](62q05.md "MISSING PAGE")
                                                                  ## [Numerical analysis](65-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](65-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](65-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](65-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](65-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](65-04.md "MISSING PAGE")
                                                                                  - [Experimental papers](65-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](65-06.md "MISSING PAGE")
                                                                                  - [Tables](65a05.md "MISSING PAGE")
                                                                                  - [Acceleration of convergence](65bxx.md "MISSING PAGE")
                                                                                  - [Extrapolation to the limit, deferred corrections](65b05.md "MISSING PAGE")
                                                                                  - [Summation of series](65b10.md "MISSING PAGE")
                                                                                  - [Euler-Maclaurin formula](65b15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65b99.md "MISSING PAGE")
                                                                                  - [Probabilistic methods, simulation and stochastic differential equations](65cxx.md "MISSING PAGE")
                                                                                  - [Monte Carlo methods](65c05.md "MISSING PAGE")
                                                                                  - [Random number generation](65c10.md "MISSING PAGE")
                                                                                  - [Models, numerical methods](65c20.md "MISSING PAGE")
                                                                                  - [Stochastic differential and integral equations](65c30.md "MISSING PAGE")
                                                                                  - [Stochastic particle methods](65c35.md "MISSING PAGE")
                                                                                  - [Computational Markov chains](65c40.md "MISSING PAGE")
                                                                                  - [Other computational problems in probability](65c50.md "MISSING PAGE")
                                                                                  - [Computational problems in statistics](65c60.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65c99.md "MISSING PAGE")
                                                                                  - [Numerical approximation and computational geometry {Primarily algorithms; for theory, see 41-XX and 68Uxx]](65dxx.md "MISSING PAGE")
                                                                                  - [Interpolation](65d05.md "MISSING PAGE")
                                                                                  - [Splines](65d07.md "MISSING PAGE")
                                                                                  - [Smoothing, curve fitting](65d10.md "MISSING PAGE")
                                                                                  - [Algorithms for functional approximation](65d15.md "MISSING PAGE")
                                                                                  - [Computer aided design (modeling of curves and surfaces)](65d17.md "MISSING PAGE")
                                                                                  - [Computer graphics and computational geometry](65d18.md "MISSING PAGE")
                                                                                  - [Computation of special functions, construction of tables](65d20.md "MISSING PAGE")
                                                                                  - [Numerical differentiation](65d25.md "MISSING PAGE")
                                                                                  - [Numerical integration](65d30.md "MISSING PAGE")
                                                                                  - [Quadrature and cubature formulas](65d32.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65d99.md "MISSING PAGE")
                                                                                  - [Numerical methods in complex analysis (potential theory, etc.)](65e05.md "MISSING PAGE")
                                                                                  - [Numerical linear algebra](65fxx.md "MISSING PAGE")
                                                                                  - [Direct methods for linear systems and matrix inversion](65f05.md "MISSING PAGE")
                                                                                  - [Iterative methods for linear systems](65f10.md "MISSING PAGE")
                                                                                  - [Eigenvalues, eigenvectors](65f15.md "MISSING PAGE")
                                                                                  - [Inverse eigenvalue problems](65f18.md "MISSING PAGE")
                                                                                  - [Overdetermined systems, pseudoinverses](65f20.md "MISSING PAGE")
                                                                                  - [Ill-posedness, regularization](65f22.md "MISSING PAGE")
                                                                                  - [Orthogonalization](65f25.md "MISSING PAGE")
                                                                                  - [Other matrix algorithms](65f30.md "MISSING PAGE")
                                                                                  - [Matrix norms, conditioning, scaling](65f35.md "MISSING PAGE")
                                                                                  - [Determinants](65f40.md "MISSING PAGE")
                                                                                  - [Sparse matrices](65f50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65f99.md "MISSING PAGE")
                                                                                  - [Error analysis and interval analysis](65gxx.md "MISSING PAGE")
                                                                                  - [Algorithms with automatic result verification](65g20.md "MISSING PAGE")
                                                                                  - [Interval and finite arithmetic](65g30.md "MISSING PAGE")
                                                                                  - [General methods in interval analysis](65g40.md "MISSING PAGE")
                                                                                  - [Roundoff error](65g50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65g99.md "MISSING PAGE")
                                                                                  - [Nonlinear algebraic or transcendental equations](65hxx.md "MISSING PAGE")
                                                                                  - [Single equations](65h05.md "MISSING PAGE")
                                                                                  - [Systems of equations](65h10.md "MISSING PAGE")
                                                                                  - [Eigenvalues, eigenvectors](65h17.md "MISSING PAGE")
                                                                                  - [Global methods, including homotopy approaches](65h20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65h99.md "MISSING PAGE")
                                                                                  - [Numerical analysis in abstract spaces](65jxx.md "MISSING PAGE")
                                                                                  - [General theory](65j05.md "MISSING PAGE")
                                                                                  - [Equations with linear operators (do not use 65Fxx)](65j10.md "MISSING PAGE")
                                                                                  - [Equations with nonlinear operators (do not use 65Hxx)](65j15.md "MISSING PAGE")
                                                                                  - [Improperly posed problems; regularization](65j20.md "MISSING PAGE")
                                                                                  - [Inverse problems](65j22.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65j99.md "MISSING PAGE")
                                                                                  - [Mathematical programming, optimization and variational techniques](65kxx.md "MISSING PAGE")
                                                                                  - [Mathematical programming {Algorithms; for theory see 90Cxx]](65k05.md "MISSING PAGE")
                                                                                  - [Optimization and variational techniques](65k10.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65k99.md "MISSING PAGE")
                                                                                  - [Ordinary differential equations](65lxx.md "MISSING PAGE")
                                                                                  - [Initial value problems](65l05.md "MISSING PAGE")
                                                                                  - [Multistep, Runge-Kutta and extrapolation methods](65l06.md "MISSING PAGE")
                                                                                  - [Numerical investigation of stability of solutions](65l07.md "MISSING PAGE")
                                                                                  - [Improperly posed problems](65l08.md "MISSING PAGE")
                                                                                  - [Inverse problems](65l09.md "MISSING PAGE")
                                                                                  - [Boundary value problems](65l10.md "MISSING PAGE")
                                                                                  - [Finite difference methods](65l12.md "MISSING PAGE")
                                                                                  - [Eigenvalue problems](65l15.md "MISSING PAGE")
                                                                                  - [Stability and convergence of numerical methods](65l20.md "MISSING PAGE")
                                                                                  - [Mesh generation and refinement](65l50.md "MISSING PAGE")
                                                                                  - [Finite elements, Rayleigh-Ritz, Galerkin and collocation methods](65l60.md "MISSING PAGE")
                                                                                  - [Error bounds](65l70.md "MISSING PAGE")
                                                                                  - [Methods for differential-algebraic equations](65l80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65l99.md "MISSING PAGE")
                                                                                  - [Partial differential equations, initial value and time-dependent initial-boundary value problems](65mxx.md "MISSING PAGE")
                                                                                  - [Finite difference methods](65m06.md "MISSING PAGE")
                                                                                  - [Stability and convergence of numerical methods](65m12.md "MISSING PAGE")
                                                                                  - [Error bounds](65m15.md "MISSING PAGE")
                                                                                  - [Method of lines](65m20.md "MISSING PAGE")
                                                                                  - [Method of characteristics](65m25.md "MISSING PAGE")
                                                                                  - [Improperly posed problems](65m30.md "MISSING PAGE")
                                                                                  - [Inverse problems](65m32.md "MISSING PAGE")
                                                                                  - [Mesh generation and refinement](65m50.md "MISSING PAGE")
                                                                                  - [Multigrid methods; domain decomposition](65m55.md "MISSING PAGE")
                                                                                  - [Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods](65m60.md "MISSING PAGE")
                                                                                  - [Spectral, collocation and related methods](65m70.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65m99.md "MISSING PAGE")
                                                                                  - [Partial differential equations, boundary value problems](65nxx.md "MISSING PAGE")
                                                                                  - [Finite difference methods](65n06.md "MISSING PAGE")
                                                                                  - [Stability and convergence of numerical methods](65n12.md "MISSING PAGE")
                                                                                  - [Error bounds](65n15.md "MISSING PAGE")
                                                                                  - [Inverse problems](65n21.md "MISSING PAGE")
                                                                                  - [Solution of discretized equations](65n22.md "MISSING PAGE")
                                                                                  - [Eigenvalue problems](65n25.md "MISSING PAGE")
                                                                                  - [Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods](65n30.md "MISSING PAGE")
                                                                                  - [Spectral, collocation and related methods](65n35.md "MISSING PAGE")
                                                                                  - [Boundary element methods](65n38.md "MISSING PAGE")
                                                                                  - [Method of lines](65n40.md "MISSING PAGE")
                                                                                  - [Method of contraction of the boundary](65n45.md "MISSING PAGE")
                                                                                  - [Mesh generation and refinement](65n50.md "MISSING PAGE")
                                                                                  - [Multigrid methods; domain decomposition](65n55.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65n99.md "MISSING PAGE")
                                                                                  - [Numerical problems in dynamical systems](65pxx.md "MISSING PAGE")
                                                                                  - [Hamiltonian systems including symplectic integrators](65p10.md "MISSING PAGE")
                                                                                  - [Numerical chaos](65p20.md "MISSING PAGE")
                                                                                  - [Bifurcation problems](65p30.md "MISSING PAGE")
                                                                                  - [Nonlinear stabilities](65p40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65p99.md "MISSING PAGE")
                                                                                  - [Difference and functional equations, recurrence relations](65q05.md "MISSING PAGE")
                                                                                  - [Integral equations, integral transforms](65rxx.md "MISSING PAGE")
                                                                                  - [Integral transforms](65r10.md "MISSING PAGE")
                                                                                  - [Integral equations](65r20.md "MISSING PAGE")
                                                                                  - [Improperly posed problems](65r30.md "MISSING PAGE")
                                                                                  - [Inverse problems](65r32.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65r99.md "MISSING PAGE")
                                                                                  - [Graphical methods](65s05.md "MISSING PAGE")
                                                                                  - [Numerical methods in Fourier analysis](65txx.md "MISSING PAGE")
                                                                                  - [Trigonometric approximation and interpolation](65t40.md "MISSING PAGE")
                                                                                  - [Discrete and fast Fourier transforms](65t50.md "MISSING PAGE")
                                                                                  - [Wavelets](65t60.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65t99.md "MISSING PAGE")
                                                                                  - [Computer aspects of numerical algorithms](65yxx.md "MISSING PAGE")
                                                                                  - [Parallel computation](65y05.md "MISSING PAGE")
                                                                                  - [Algorithms for specific classes of architectures](65y10.md "MISSING PAGE")
                                                                                  - [Packaged methods](65y15.md "MISSING PAGE")
                                                                                  - [Complexity and performance of numerical algorithms](65y20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](65y99.md "MISSING PAGE")
                                                                                  - [Applications to physics](65z05.md "MISSING PAGE")
                                                                  ## [Computer science](68-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](68-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](68-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](68-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](68-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](68-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](68-06.md "MISSING PAGE")
                                                                                  - [Computer system organization](68mxx.md "MISSING PAGE")
                                                                                  - [General](68m01.md "MISSING PAGE")
                                                                                  - [Mathematical problems of computer architecture](68m07.md "MISSING PAGE")
                                                                                  - [Network design and communication](68m10.md "MISSING PAGE")
                                                                                  - [Network protocols](68m12.md "MISSING PAGE")
                                                                                  - [Distributed systems](68m14.md "MISSING PAGE")
                                                                                  - [Reliability, testing and fault tolerance](68m15.md "MISSING PAGE")
                                                                                  - [Performance evaluation; queueing; scheduling](68m20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68m99.md "MISSING PAGE")
                                                                  ## [Software](68nxx.md "MISSING PAGE")
                                                                                  - [General](68n01.md "MISSING PAGE")
                                                                                  - [Programming languages](68n15.md "MISSING PAGE")
                                                                                  - [Logic programming](68n17.md "MISSING PAGE")
                                                                                  - [Functional programming and lambda calculus](68n18.md "MISSING PAGE")
                                                                                  - [Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)](68n19.md "MISSING PAGE")
                                                                                  - [Compilers and interpreters](68n20.md "MISSING PAGE")
                                                                                  - [Operating systems](68n25.md "MISSING PAGE")
                                                                                  - [Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)](68n30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68n99.md "MISSING PAGE")
                                                                                  - [Theory of data](68pxx.md "MISSING PAGE")
                                                                                  - [General](68p01.md "MISSING PAGE")
                                                                                  - [Data structures](68p05.md "MISSING PAGE")
                                                                                  - [Searching and sorting](68p10.md "MISSING PAGE")
                                                                                  - [Database theory](68p15.md "MISSING PAGE")
                                                                                  - [Information storage and retrieval](68p20.md "MISSING PAGE")
                                                                                  - [Data encryption](68p25.md "MISSING PAGE")
                                                                                  - [Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.)](68p30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68p99.md "MISSING PAGE")
                                                                                  - [Theory of computing](68qxx.md "MISSING PAGE")
                                                                                  - [General](68q01.md "MISSING PAGE")
                                                                                  - [Models of computation (Turing machines, etc.)](68q05.md "MISSING PAGE")
                                                                                  - [Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)](68q10.md "MISSING PAGE")
                                                                                  - [Complexity classes (hierarchies, relations among complexity classes, etc.)](68q15.md "MISSING PAGE")
                                                                                  - [Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)](68q17.md "MISSING PAGE")
                                                                                  - [Descriptive complexity and finite models](68q19.md "MISSING PAGE")
                                                                                  - [Analysis of algorithms and problem complexity](68q25.md "MISSING PAGE")
                                                                                  - [Algorithmic information theory (Kolmogorov complexity, etc.)](68q30.md "MISSING PAGE")
                                                                                  - [Computational learning theory](68q32.md "MISSING PAGE")
                                                                                  - [Grammars and rewriting systems](68q42.md "MISSING PAGE")
                                                                                  - [Formal languages and automata](68q45.md "MISSING PAGE")
                                                                                  - [Semantics](68q55.md "MISSING PAGE")
                                                                                  - [Specification and verification (program logics, model checking, etc.)](68q60.md "MISSING PAGE")
                                                                                  - [Abstract data types; algebraic specification](68q65.md "MISSING PAGE")
                                                                                  - [Algebraic theory of languages and automata](68q70.md "MISSING PAGE")
                                                                                  - [Cellular automata](68q80.md "MISSING PAGE")
                                                                                  - [Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)](68q85.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68q99.md "MISSING PAGE")
                                                                                  - [Discrete mathematics in relation to computer science](68rxx.md "MISSING PAGE")
                                                                                  - [General](68r01.md "MISSING PAGE")
                                                                                  - [Combinatorics](68r05.md "MISSING PAGE")
                                                                                  - [Graph theory](68r10.md "MISSING PAGE")
                                                                                  - [Combinatorics on words](68r15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68r99.md "MISSING PAGE")
                                                                                  - [Artificial intelligence](68txx.md "MISSING PAGE")
                                                                                  - [General](68t01.md "MISSING PAGE")
                                                                                  - [Learning and adaptive systems](68t05.md "MISSING PAGE")
                                                                                  - [Pattern recognition, speech recognition](68t10.md "MISSING PAGE")
                                                                                  - [Theorem proving (deduction, resolution, etc.)](68t15.md "MISSING PAGE")
                                                                                  - [Problem solving (heuristics, search strategies, etc.)](68t20.md "MISSING PAGE")
                                                                                  - [Logic in artificial intelligence](68t27.md "MISSING PAGE")
                                                                                  - [Knowledge representation](68t30.md "MISSING PAGE")
                                                                                  - [Languages and software systems (knowledge-based systems, expert systems, etc.)](68t35.md "MISSING PAGE")
                                                                                  - [Reasoning under uncertainty](68t37.md "MISSING PAGE")
                                                                                  - [Robotics](68t40.md "MISSING PAGE")
                                                                                  - [Machine vision and scene understanding](68t45.md "MISSING PAGE")
                                                                                  - [Natural language processing](68t50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68t99.md "MISSING PAGE")
                                                                                  - [Computing methodologies and applications](68uxx.md "MISSING PAGE")
                                                                                  - [General](68u01.md "MISSING PAGE")
                                                                                  - [Computer graphics; computational geometry](68u05.md "MISSING PAGE")
                                                                                  - [Computer-aided design](68u07.md "MISSING PAGE")
                                                                                  - [Image processing](68u10.md "MISSING PAGE")
                                                                                  - [Text processing; mathematical typography](68u15.md "MISSING PAGE")
                                                                                  - [Simulation](68u20.md "MISSING PAGE")
                                                                                  - [Information systems (hypertext navigation, interfaces, decision support, etc.)](68u35.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68u99.md "MISSING PAGE")
                                                                  ## [Algorithms](68wxx.md "MISSING PAGE")
                                                                                  - [General](68w01.md "MISSING PAGE")
                                                                                  - [Nonnumerical algorithms](68w05.md "MISSING PAGE")
                                                                                  - [Parallel algorithms](68w10.md "MISSING PAGE")
                                                                                  - [Distributed algorithms](68w15.md "MISSING PAGE")
                                                                                  - [Randomized algorithms](68w20.md "MISSING PAGE")
                                                                                  - [Approximation algorithms](68w25.md "MISSING PAGE")
                                                                                  - [Symbolic computation and algebraic computation](68w30.md "MISSING PAGE")
                                                                                  - [VLSI algorithms](68w35.md "MISSING PAGE")
                                                                                  - [Analysis of algorithms](68w40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](68w99.md "MISSING PAGE")
                                                                  ## [Mechanics of particles and systems](70-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](70-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](70-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](70-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](70-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](70-04.md "MISSING PAGE")
                                                                                  - [Experimental work](70-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](70-06.md "MISSING PAGE")
                                                                                  - [Computational methods](70-08.md "MISSING PAGE")
                                                                                  - [Axiomatics, foundations](70a05.md "MISSING PAGE")
                                                                                  - [Kinematics](70bxx.md "MISSING PAGE")
                                                                                  - [Kinematics of a particle](70b05.md "MISSING PAGE")
                                                                                  - [Kinematics of a rigid body](70b10.md "MISSING PAGE")
                                                                                  - [Mechanisms, robots](70b15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70b99.md "MISSING PAGE")
                                                                                  - [Statics](70c20.md "MISSING PAGE")
                                                                                  - [Dynamics of a rigid body and of multibody systems](70exx.md "MISSING PAGE")
                                                                                  - [Motion of the gyroscope](70e05.md "MISSING PAGE")
                                                                                  - [Free motion of a rigid body](70e15.md "MISSING PAGE")
                                                                                  - [Motion of a rigid body with a fixed point](70e17.md "MISSING PAGE")
                                                                                  - [Motion of a rigid body in contact with a solid surface](70e18.md "MISSING PAGE")
                                                                                  - [Perturbation methods for rigid body dynamics](70e20.md "MISSING PAGE")
                                                                                  - [Integrable cases of motion](70e40.md "MISSING PAGE")
                                                                                  - [Higher-dimensional generalizations](70e45.md "MISSING PAGE")
                                                                                  - [Stability problems](70e50.md "MISSING PAGE")
                                                                                  - [Dynamics of multibody systems](70e55.md "MISSING PAGE")
                                                                                  - [Robot dynamics and control](70e60.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70e99.md "MISSING PAGE")
                                                                                  - [Dynamics of a system of particles, including celestial mechanics](70fxx.md "MISSING PAGE")
                                                                                  - [Two-body problems](70f05.md "MISSING PAGE")
                                                                                  - [Three-body problems](70f07.md "MISSING PAGE")
                                                                                  - [$n$-body problems](70f10.md "MISSING PAGE")
                                                                                  - [Celestial mechanics](70f15.md "MISSING PAGE")
                                                                                  - [Collisions in celestial mechanics, regularization](70f16.md "MISSING PAGE")
                                                                                  - [Inverse problems](70f17.md "MISSING PAGE")
                                                                                  - [Holonomic systems](70f20.md "MISSING PAGE")
                                                                                  - [Nonholonomic systems](70f25.md "MISSING PAGE")
                                                                                  - [Collision of rigid or pseudo-rigid bodies](70f35.md "MISSING PAGE")
                                                                                  - [Problems with friction](70f40.md "MISSING PAGE")
                                                                                  - [Infinite particle systems](70f45.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70f99.md "MISSING PAGE")
                                                                                  - [General models, approaches, and methods](70gxx.md "MISSING PAGE")
                                                                                  - [Generalized coordinates; event, impulse-energy, configuration, state, or phase space](70g10.md "MISSING PAGE")
                                                                                  - [Topological and differential-topological methods](70g40.md "MISSING PAGE")
                                                                                  - [Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.)](70g45.md "MISSING PAGE")
                                                                                  - [Algebraic geometry methods](70g55.md "MISSING PAGE")
                                                                                  - [Dynamical systems methods](70g60.md "MISSING PAGE")
                                                                                  - [Symmetries, Lie-group and Lie-algebra methods](70g65.md "MISSING PAGE")
                                                                                  - [Functional-analytic methods](70g70.md "MISSING PAGE")
                                                                                  - [Variational methods](70g75.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70g99.md "MISSING PAGE")
                                                                                  - [Hamiltonian and Lagrangian mechanics](70hxx.md "MISSING PAGE")
                                                                                  - [Lagrange's equations](70h03.md "MISSING PAGE")
                                                                                  - [Hamilton's equations](70h05.md "MISSING PAGE")
                                                                                  - [Completely integrable systems and methods of integration](70h06.md "MISSING PAGE")
                                                                                  - [Nonintegrable systems](70h07.md "MISSING PAGE")
                                                                                  - [Nearly integrable Hamiltonian systems, KAM theory](70h08.md "MISSING PAGE")
                                                                                  - [Perturbation theories](70h09.md "MISSING PAGE")
                                                                                  - [Adiabatic invariants](70h11.md "MISSING PAGE")
                                                                                  - [Periodic and almost periodic solutions](70h12.md "MISSING PAGE")
                                                                                  - [Stability problems](70h14.md "MISSING PAGE")
                                                                                  - [Canonical and symplectic transformations](70h15.md "MISSING PAGE")
                                                                                  - [Hamilton-Jacobi equations](70h20.md "MISSING PAGE")
                                                                                  - [Hamilton's principle](70h25.md "MISSING PAGE")
                                                                                  - [Other variational principles](70h30.md "MISSING PAGE")
                                                                                  - [Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction](70h33.md "MISSING PAGE")
                                                                                  - [Relativistic dynamics](70h40.md "MISSING PAGE")
                                                                                  - [Constrained dynamics, Dirac's theory of constraints](70h45.md "MISSING PAGE")
                                                                                  - [Higher-order theories](70h50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70h99.md "MISSING PAGE")
                                                                                  - [Linear vibration theory](70jxx.md "MISSING PAGE")
                                                                                  - [Modal analysis](70j10.md "MISSING PAGE")
                                                                                  - [Stability](70j25.md "MISSING PAGE")
                                                                                  - [Free motions](70j30.md "MISSING PAGE")
                                                                                  - [Forced motions](70j35.md "MISSING PAGE")
                                                                                  - [Parametric resonances](70j40.md "MISSING PAGE")
                                                                                  - [Systems arising from the discretization of structural vibration problems](70j50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70j99.md "MISSING PAGE")
                                                                                  - [Nonlinear dynamics](70kxx.md "MISSING PAGE")
                                                                                  - [Phase plane analysis, limit cycles](70k05.md "MISSING PAGE")
                                                                                  - [Stability](70k20.md "MISSING PAGE")
                                                                                  - [Free motions](70k25.md "MISSING PAGE")
                                                                                  - [Parametric resonances](70k28.md "MISSING PAGE")
                                                                                  - [Nonlinear resonances](70k30.md "MISSING PAGE")
                                                                                  - [Forced motions](70k40.md "MISSING PAGE")
                                                                                  - [Equilibria and periodic trajectories](70k42.md "MISSING PAGE")
                                                                                  - [Quasi-periodic motions and invariant tori](70k43.md "MISSING PAGE")
                                                                                  - [Homoclinic and heteroclinic trajectories](70k44.md "MISSING PAGE")
                                                                                  - [Normal forms](70k45.md "MISSING PAGE")
                                                                                  - [Bifurcations and instability](70k50.md "MISSING PAGE")
                                                                                  - [Transition to stochasticity (chaotic behavior)](70k55.md "MISSING PAGE")
                                                                                  - [General perturbation schemes](70k60.md "MISSING PAGE")
                                                                                  - [Averaging of perturbations](70k65.md "MISSING PAGE")
                                                                                  - [Systems with slow and fast motions](70k70.md "MISSING PAGE")
                                                                                  - [Nonlinear modes](70k75.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70k99.md "MISSING PAGE")
                                                                                  - [Random vibrations](70l05.md "MISSING PAGE")
                                                                                  - [Orbital mechanics](70m20.md "MISSING PAGE")
                                                                                  - [Variable mass, rockets](70p05.md "MISSING PAGE")
                                                                                  - [Control of mechanical systems](70q05.md "MISSING PAGE")
                                                                                  - [Classical field theories](70sxx.md "MISSING PAGE")
                                                                                  - [Lagrangian formalism and Hamiltonian formalism](70s05.md "MISSING PAGE")
                                                                                  - [Symmetries and conservation laws](70s10.md "MISSING PAGE")
                                                                                  - [Yang-Mills and other gauge theories](70s15.md "MISSING PAGE")
                                                                                  - [More general nonquantum field theories](70s20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](70s99.md "MISSING PAGE")
                                                                  ## [Mechanics of deformable solids](74-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](74-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](74-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](74-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](74-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](74-04.md "MISSING PAGE")
                                                                                  - [Experimental work](74-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](74-06.md "MISSING PAGE")
                                                                                  - [Generalities, axiomatics, foundations of continuum mechanics of solids](74axx.md "MISSING PAGE")
                                                                                  - [Kinematics of deformation](74a05.md "MISSING PAGE")
                                                                                  - [Stress](74a10.md "MISSING PAGE")
                                                                                  - [Thermodynamics](74a15.md "MISSING PAGE")
                                                                                  - [Theory of constitutive functions](74a20.md "MISSING PAGE")
                                                                                  - [Molecular, statistical, and kinetic theories](74a25.md "MISSING PAGE")
                                                                                  - [Nonsimple materials](74a30.md "MISSING PAGE")
                                                                                  - [Polar materials](74a35.md "MISSING PAGE")
                                                                                  - [Random materials and composite materials](74a40.md "MISSING PAGE")
                                                                                  - [Theories of fracture and damage](74a45.md "MISSING PAGE")
                                                                                  - [Structured surfaces and interfaces, coexistent phases](74a50.md "MISSING PAGE")
                                                                                  - [Theories of friction (tribology)](74a55.md "MISSING PAGE")
                                                                                  - [Micromechanical theories](74a60.md "MISSING PAGE")
                                                                                  - [Reactive materials](74a65.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74a99.md "MISSING PAGE")
                                                                                  - [Elastic materials](74bxx.md "MISSING PAGE")
                                                                                  - [Classical linear elasticity](74b05.md "MISSING PAGE")
                                                                                  - [Linear elasticity with initial stresses](74b10.md "MISSING PAGE")
                                                                                  - [Equations linearized about a deformed state (small deformations superposed on large)](74b15.md "MISSING PAGE")
                                                                                  - [Nonlinear elasticity](74b20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74b99.md "MISSING PAGE")
                                                                                  - [Plastic materials, materials of stress-rate and internal-variable type](74cxx.md "MISSING PAGE")
                                                                                  - [Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)](74c05.md "MISSING PAGE")
                                                                                  - [Small-strain, rate-dependent theories (including theories of viscoplasticity)](74c10.md "MISSING PAGE")
                                                                                  - [Large-strain, rate-independent theories (including nonlinear plasticity)](74c15.md "MISSING PAGE")
                                                                                  - [Large-strain, rate-dependent theories](74c20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74c99.md "MISSING PAGE")
                                                                                  - [Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)](74dxx.md "MISSING PAGE")
                                                                                  - [Linear constitutive equations](74d05.md "MISSING PAGE")
                                                                                  - [Nonlinear constitutive equations](74d10.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74d99.md "MISSING PAGE")
                                                                                  - [Material properties given special treatment](74exx.md "MISSING PAGE")
                                                                                  - [Inhomogeneity](74e05.md "MISSING PAGE")
                                                                                  - [Anisotropy](74e10.md "MISSING PAGE")
                                                                                  - [Crystalline structure](74e15.md "MISSING PAGE")
                                                                                  - [Granularity](74e20.md "MISSING PAGE")
                                                                                  - [Texture](74e25.md "MISSING PAGE")
                                                                                  - [Composite and mixture properties](74e30.md "MISSING PAGE")
                                                                                  - [Random structure](74e35.md "MISSING PAGE")
                                                                                  - [Chemical structure](74e40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74e99.md "MISSING PAGE")
                                                                                  - [Coupling of solid mechanics with other effects](74fxx.md "MISSING PAGE")
                                                                                  - [Thermal effects](74f05.md "MISSING PAGE")
                                                                                  - [Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)](74f10.md "MISSING PAGE")
                                                                                  - [Electromagnetic effects](74f15.md "MISSING PAGE")
                                                                                  - [Mixture effects](74f20.md "MISSING PAGE")
                                                                                  - [Chemical and reactive effects](74f25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74f99.md "MISSING PAGE")
                                                                                  - [Equilibrium (steady-state) problems](74gxx.md "MISSING PAGE")
                                                                                  - [Explicit solutions](74g05.md "MISSING PAGE")
                                                                                  - [Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)](74g10.md "MISSING PAGE")
                                                                                  - [Numerical approximation of solutions](74g15.md "MISSING PAGE")
                                                                                  - [Local existence of solutions (near a given solution)](74g20.md "MISSING PAGE")
                                                                                  - [Global existence of solutions](74g25.md "MISSING PAGE")
                                                                                  - [Uniqueness of solutions](74g30.md "MISSING PAGE")
                                                                                  - [Multiplicity of solutions](74g35.md "MISSING PAGE")
                                                                                  - [Regularity of solutions](74g40.md "MISSING PAGE")
                                                                                  - [Bounds for solutions](74g45.md "MISSING PAGE")
                                                                                  - [Saint-Venant's principle](74g50.md "MISSING PAGE")
                                                                                  - [Qualitative behavior of solutions](74g55.md "MISSING PAGE")
                                                                                  - [Bifurcation and buckling](74g60.md "MISSING PAGE")
                                                                                  - [Energy minimization](74g65.md "MISSING PAGE")
                                                                                  - [Stress concentrations, singularities](74g70.md "MISSING PAGE")
                                                                                  - [Inverse problems](74g75.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74g99.md "MISSING PAGE")
                                                                                  - [Dynamical problems](74hxx.md "MISSING PAGE")
                                                                                  - [Explicit solutions](74h05.md "MISSING PAGE")
                                                                                  - [Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)](74h10.md "MISSING PAGE")
                                                                                  - [Numerical approximation of solutions](74h15.md "MISSING PAGE")
                                                                                  - [Existence of solutions](74h20.md "MISSING PAGE")
                                                                                  - [Uniqueness of solutions](74h25.md "MISSING PAGE")
                                                                                  - [Regularity of solutions](74h30.md "MISSING PAGE")
                                                                                  - [Singularities, blowup, stress concentrations](74h35.md "MISSING PAGE")
                                                                                  - [Long-time behavior of solutions](74h40.md "MISSING PAGE")
                                                                                  - [Vibrations](74h45.md "MISSING PAGE")
                                                                                  - [Random vibrations](74h50.md "MISSING PAGE")
                                                                                  - [Stability](74h55.md "MISSING PAGE")
                                                                                  - [Dynamical bifurcation](74h60.md "MISSING PAGE")
                                                                                  - [Chaotic behavior](74h65.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74h99.md "MISSING PAGE")
                                                                                  - [Waves](74jxx.md "MISSING PAGE")
                                                                                  - [Linear waves](74j05.md "MISSING PAGE")
                                                                                  - [Bulk waves](74j10.md "MISSING PAGE")
                                                                                  - [Surface waves](74j15.md "MISSING PAGE")
                                                                                  - [Wave scattering](74j20.md "MISSING PAGE")
                                                                                  - [Inverse problems](74j25.md "MISSING PAGE")
                                                                                  - [Nonlinear waves](74j30.md "MISSING PAGE")
                                                                                  - [Solitary waves](74j35.md "MISSING PAGE")
                                                                                  - [Shocks and related discontinuities](74j40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74j99.md "MISSING PAGE")
                                                                                  - [Thin bodies, structures](74kxx.md "MISSING PAGE")
                                                                                  - [Strings](74k05.md "MISSING PAGE")
                                                                                  - [Rods (beams, columns, shafts, arches, rings, etc.)](74k10.md "MISSING PAGE")
                                                                                  - [Membranes](74k15.md "MISSING PAGE")
                                                                                  - [Plates](74k20.md "MISSING PAGE")
                                                                                  - [Shells](74k25.md "MISSING PAGE")
                                                                                  - [Junctions](74k30.md "MISSING PAGE")
                                                                                  - [Thin films](74k35.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74k99.md "MISSING PAGE")
                                                                                  - [Special subfields of solid mechanics](74lxx.md "MISSING PAGE")
                                                                                  - [Geophysical solid mechanics](74l05.md "MISSING PAGE")
                                                                                  - [Soil and rock mechanics](74l10.md "MISSING PAGE")
                                                                                  - [Biomechanical solid mechanics](74l15.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74l99.md "MISSING PAGE")
                                                                                  - [Special kinds of problems](74mxx.md "MISSING PAGE")
                                                                                  - [Control, switches and devices (``smart materials'')](74m05.md "MISSING PAGE")
                                                                                  - [Friction](74m10.md "MISSING PAGE")
                                                                                  - [Contact](74m15.md "MISSING PAGE")
                                                                                  - [Impact](74m20.md "MISSING PAGE")
                                                                                  - [Micromechanics](74m25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74m99.md "MISSING PAGE")
                                                                                  - [Phase transformations in solids](74nxx.md "MISSING PAGE")
                                                                                  - [Crystals](74n05.md "MISSING PAGE")
                                                                                  - [Displacive transformations](74n10.md "MISSING PAGE")
                                                                                  - [Analysis of microstructure](74n15.md "MISSING PAGE")
                                                                                  - [Dynamics of phase boundaries](74n20.md "MISSING PAGE")
                                                                                  - [Transformations involving diffusion](74n25.md "MISSING PAGE")
                                                                                  - [Problems involving hysteresis](74n30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74n99.md "MISSING PAGE")
                                                                                  - [Optimization](74pxx.md "MISSING PAGE")
                                                                                  - [Compliance or weight optimization](74p05.md "MISSING PAGE")
                                                                                  - [Optimization of other properties](74p10.md "MISSING PAGE")
                                                                                  - [Topological methods](74p15.md "MISSING PAGE")
                                                                                  - [Geometrical methods](74p20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74p99.md "MISSING PAGE")
                                                                                  - [Homogenization, determination of effective properties](74qxx.md "MISSING PAGE")
                                                                                  - [Homogenization in equilibrium problems](74q05.md "MISSING PAGE")
                                                                                  - [Homogenization and oscillations in dynamical problems](74q10.md "MISSING PAGE")
                                                                                  - [Effective constitutive equations](74q15.md "MISSING PAGE")
                                                                                  - [Bounds on effective properties](74q20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74q99.md "MISSING PAGE")
                                                                                  - [Fracture and damage](74rxx.md "MISSING PAGE")
                                                                                  - [Brittle damage](74r05.md "MISSING PAGE")
                                                                                  - [Brittle fracture](74r10.md "MISSING PAGE")
                                                                                  - [High-velocity fracture](74r15.md "MISSING PAGE")
                                                                                  - [Anelastic fracture and damage](74r20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74r99.md "MISSING PAGE")
                                                                                  - [Numerical methods](74sxx.md "MISSING PAGE")
                                                                                  - [Finite element methods](74s05.md "MISSING PAGE")
                                                                                  - [Finite volume methods](74s10.md "MISSING PAGE")
                                                                                  - [Boundary element methods](74s15.md "MISSING PAGE")
                                                                                  - [Finite difference methods](74s20.md "MISSING PAGE")
                                                                                  - [Spectral and related methods](74s25.md "MISSING PAGE")
                                                                                  - [Other numerical methods](74s30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](74s99.md "MISSING PAGE")
                                                                                  - [Fluid mechanics](76-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](76-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](76-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](76-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](76-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](76-04.md "MISSING PAGE")
                                                                                  - [Experimental work](76-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](76-06.md "MISSING PAGE")
                                                                                  - [Foundations, constitutive equations, rheology](76axx.md "MISSING PAGE")
                                                                                  - [Foundations of fluid mechanics](76a02.md "MISSING PAGE")
                                                                                  - [Non-Newtonian fluids](76a05.md "MISSING PAGE")
                                                                                  - [Viscoelastic fluids](76a10.md "MISSING PAGE")
                                                                                  - [Liquid crystals](76a15.md "MISSING PAGE")
                                                                                  - [Thin fluid films](76a20.md "MISSING PAGE")
                                                                                  - [Superfluids (classical aspects)](76a25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76a99.md "MISSING PAGE")
                                                                                  - [Incompressible inviscid fluids](76bxx.md "MISSING PAGE")
                                                                                  - [Existence, uniqueness, and regularity theory](76b03.md "MISSING PAGE")
                                                                                  - [Free-surface potential flows](76b07.md "MISSING PAGE")
                                                                                  - [Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing](76b10.md "MISSING PAGE")
                                                                                  - [Water waves, gravity waves; dispersion and scattering, nonlinear interaction](76b15.md "MISSING PAGE")
                                                                                  - [Ship waves](76b20.md "MISSING PAGE")
                                                                                  - [Solitary waves](76b25.md "MISSING PAGE")
                                                                                  - [Capillarity (surface tension)](76b45.md "MISSING PAGE")
                                                                                  - [Vortex flows](76b47.md "MISSING PAGE")
                                                                                  - [Internal waves](76b55.md "MISSING PAGE")
                                                                                  - [Atmospheric waves](76b60.md "MISSING PAGE")
                                                                                  - [Rossby waves](76b65.md "MISSING PAGE")
                                                                                  - [Stratification effects in inviscid fluids](76b70.md "MISSING PAGE")
                                                                                  - [Flow control and optimization](76b75.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76b99.md "MISSING PAGE")
                                                                                  - [Incompressible viscous fluids](76dxx.md "MISSING PAGE")
                                                                                  - [Existence, uniqueness, and regularity theory](76d03.md "MISSING PAGE")
                                                                                  - [Navier-Stokes equations](76d05.md "MISSING PAGE")
                                                                                  - [Statistical solutions of Navier-Stokes and related equations](76d06.md "MISSING PAGE")
                                                                                  - [Stokes and related (Oseen, etc.) flows](76d07.md "MISSING PAGE")
                                                                                  - [Lubrication theory](76d08.md "MISSING PAGE")
                                                                                  - [Viscous-inviscid interaction](76d09.md "MISSING PAGE")
                                                                                  - [Boundary-layer theory, separation and reattachment, higher-order effects](76d10.md "MISSING PAGE")
                                                                                  - [Viscous vortex flows](76d17.md "MISSING PAGE")
                                                                                  - [Wakes and jets](76d25.md "MISSING PAGE")
                                                                                  - [Other free-boundary flows; Hele-Shaw flows](76d27.md "MISSING PAGE")
                                                                                  - [Waves](76d33.md "MISSING PAGE")
                                                                                  - [Capillarity (surface tension)](76d45.md "MISSING PAGE")
                                                                                  - [Stratification effects in viscous fluids](76d50.md "MISSING PAGE")
                                                                                  - [Flow control and optimization](76d55.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76d99.md "MISSING PAGE")
                                                                                  - [Hydrodynamic stability](76exx.md "MISSING PAGE")
                                                                                  - [Parallel shear flows](76e05.md "MISSING PAGE")
                                                                                  - [Convection](76e06.md "MISSING PAGE")
                                                                                  - [Rotation](76e07.md "MISSING PAGE")
                                                                                  - [Stability and instability of nonparallel flows](76e09.md "MISSING PAGE")
                                                                                  - [Absolute and convective instability and stability](76e15.md "MISSING PAGE")
                                                                                  - [Interfacial stability and instability](76e17.md "MISSING PAGE")
                                                                                  - [Compressibility effects](76e19.md "MISSING PAGE")
                                                                                  - [Stability and instability of geophysical and astrophysical flows](76e20.md "MISSING PAGE")
                                                                                  - [Stability and instability of magnetohydrodynamic and electrohydrodynamic flows](76e25.md "MISSING PAGE")
                                                                                  - [Nonlinear effects](76e30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76e99.md "MISSING PAGE")
                                                                                  - [Turbulence](76fxx.md "MISSING PAGE")
                                                                                  - [Fundamentals](76f02.md "MISSING PAGE")
                                                                                  - [Isotropic turbulence; homogeneous turbulence](76f05.md "MISSING PAGE")
                                                                                  - [Transition to turbulence](76f06.md "MISSING PAGE")
                                                                                  - [Shear flows](76f10.md "MISSING PAGE")
                                                                                  - [Dynamical systems approach to turbulence](76f20.md "MISSING PAGE")
                                                                                  - [Turbulent transport, mixing](76f25.md "MISSING PAGE")
                                                                                  - [Renormalization and other field-theoretical methods](76f30.md "MISSING PAGE")
                                                                                  - [Convective turbulence](76f35.md "MISSING PAGE")
                                                                                  - [Turbulent boundary layers](76f40.md "MISSING PAGE")
                                                                                  - [Stratification effects](76f45.md "MISSING PAGE")
                                                                                  - [Compressibility effects](76f50.md "MISSING PAGE")
                                                                                  - [Statistical turbulence modeling](76f55.md "MISSING PAGE")
                                                                                  - [$k$-$varepsilon$ modeling](76f60.md "MISSING PAGE")
                                                                                  - [Direct numerical and large eddy simulation of turbulence](76f65.md "MISSING PAGE")
                                                                                  - [Control of turbulent flows](76f70.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76f99.md "MISSING PAGE")
                                                                                  - [General aerodynamics and subsonic flows](76g25.md "MISSING PAGE")
                                                                                  - [Transonic flows](76h05.md "MISSING PAGE")
                                                                                  - [Supersonic flows](76j20.md "MISSING PAGE")
                                                                                  - [Hypersonic flows](76k05.md "MISSING PAGE")
                                                                                  - [Shock waves and blast waves](76l05.md "MISSING PAGE")
                                                                                  - [Basic methods in fluid mechanics](76mxx.md "MISSING PAGE")
                                                                                  - [Finite element methods](76m10.md "MISSING PAGE")
                                                                                  - [Finite volume methods](76m12.md "MISSING PAGE")
                                                                                  - [Boundary element methods](76m15.md "MISSING PAGE")
                                                                                  - [Finite difference methods](76m20.md "MISSING PAGE")
                                                                                  - [Spectral methods](76m22.md "MISSING PAGE")
                                                                                  - [Vortex methods](76m23.md "MISSING PAGE")
                                                                                  - [Other numerical methods](76m25.md "MISSING PAGE")
                                                                                  - [Visualization algorithms](76m27.md "MISSING PAGE")
                                                                                  - [Particle methods and lattice-gas methods](76m28.md "MISSING PAGE")
                                                                                  - [Variational methods](76m30.md "MISSING PAGE")
                                                                                  - [Stochastic analysis](76m35.md "MISSING PAGE")
                                                                                  - [Complex-variables methods](76m40.md "MISSING PAGE")
                                                                                  - [Asymptotic methods, singular perturbations](76m45.md "MISSING PAGE")
                                                                                  - [Homogenization](76m50.md "MISSING PAGE")
                                                                                  - [Dimensional analysis and similarity](76m55.md "MISSING PAGE")
                                                                                  - [Symmetry analysis, Lie group and algebra methods](76m60.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76m99.md "MISSING PAGE")
                                                                                  - [Compressible fluids and gas dynamics, general](76nxx.md "MISSING PAGE")
                                                                                  - [Existence, uniqueness, and regularity theory](76n10.md "MISSING PAGE")
                                                                                  - [Gas dynamics, general](76n15.md "MISSING PAGE")
                                                                                  - [Viscous-inviscid interaction](76n17.md "MISSING PAGE")
                                                                                  - [Boundary-layer theory](76n20.md "MISSING PAGE")
                                                                                  - [Flow control and optimization](76n25.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76n99.md "MISSING PAGE")
                                                                                  - [Rarefied gas flows, Boltzmann equation](76p05.md "MISSING PAGE")
                                                                                  - [Hydro- and aero-acoustics](76q05.md "MISSING PAGE")
                                                                                  - [Diffusion and convection](76rxx.md "MISSING PAGE")
                                                                                  - [Forced convection](76r05.md "MISSING PAGE")
                                                                                  - [Free convection](76r10.md "MISSING PAGE")
                                                                                  - [Diffusion](76r50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76r99.md "MISSING PAGE")
                                                                                  - [Flows in porous media; filtration; seepage](76s05.md "MISSING PAGE")
                                                                                  - [Two-phase and multiphase flows](76txx.md "MISSING PAGE")
                                                                                  - [Liquid-gas two-phase flows, bubbly flows](76t10.md "MISSING PAGE")
                                                                                  - [Dusty-gas two-phase flows](76t15.md "MISSING PAGE")
                                                                                  - [Suspensions](76t20.md "MISSING PAGE")
                                                                                  - [Granular flows](76t25.md "MISSING PAGE")
                                                                                  - [Three or more component flows](76t30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76t99.md "MISSING PAGE")
                                                                                  - [Rotating fluids](76u05.md "MISSING PAGE")
                                                                                  - [Reaction effects in flows](76v05.md "MISSING PAGE")
                                                                                  - [Magnetohydrodynamics and electrohydrodynamics](76w05.md "MISSING PAGE")
                                                                                  - [Ionized gas flow in electromagnetic fields; plasmic flow](76x05.md "MISSING PAGE")
                                                                                  - [Quantum hydrodynamics and relativistic hydrodynamics](76y05.md "MISSING PAGE")
                                                                                  - [Biological fluid mechanics](76zxx.md "MISSING PAGE")
                                                                                  - [Physiological flows](76z05.md "MISSING PAGE")
                                                                                  - [Biopropulsion in water and in air](76z10.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](76z99.md "MISSING PAGE")
                                                                  ## [Optics, electromagnetic theory](78-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](78-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](78-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](78-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](78-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](78-04.md "MISSING PAGE")
                                                                                  - [Experimental work](78-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](78-06.md "MISSING PAGE")
                                                                                  - [General](78axx.md "MISSING PAGE")
                                                                                  - [Foundations](78a02.md "MISSING PAGE")
                                                                                  - [Geometric optics](78a05.md "MISSING PAGE")
                                                                                  - [Physical optics](78a10.md "MISSING PAGE")
                                                                                  - [Electron optics](78a15.md "MISSING PAGE")
                                                                                  - [Space charge waves](78a20.md "MISSING PAGE")
                                                                                  - [Electromagnetic theory, general](78a25.md "MISSING PAGE")
                                                                                  - [Electro- and magnetostatics](78a30.md "MISSING PAGE")
                                                                                  - [Motion of charged particles](78a35.md "MISSING PAGE")
                                                                                  - [Waves and radiation](78a40.md "MISSING PAGE")
                                                                                  - [Diffraction, scattering](78a45.md "MISSING PAGE")
                                                                                  - [Inverse scattering problems](78a46.md "MISSING PAGE")
                                                                                  - [Composite media; random media](78a48.md "MISSING PAGE")
                                                                                  - [Antennas, wave-guides](78a50.md "MISSING PAGE")
                                                                                  - [Technical applications](78a55.md "MISSING PAGE")
                                                                                  - [Lasers, masers, optical bistability, nonlinear optics](78a60.md "MISSING PAGE")
                                                                                  - [Biological applications](78a70.md "MISSING PAGE")
                                                                                  - [Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)](78a97.md "MISSING PAGE")
                                                                                  - [Miscellaneous topics](78a99.md "MISSING PAGE")
                                                                                  - [Basic methods](78mxx.md "MISSING PAGE")
                                                                                  - [Method of moments](78m05.md "MISSING PAGE")
                                                                                  - [Finite element methods](78m10.md "MISSING PAGE")
                                                                                  - [Boundary element methods](78m15.md "MISSING PAGE")
                                                                                  - [Finite difference methods](78m20.md "MISSING PAGE")
                                                                                  - [Other numerical methods](78m25.md "MISSING PAGE")
                                                                                  - [Variational methods](78m30.md "MISSING PAGE")
                                                                                  - [Asymptotic analysis](78m35.md "MISSING PAGE")
                                                                                  - [Homogenization](78m40.md "MISSING PAGE")
                                                                                  - [Optimization](78m50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](78m99.md "MISSING PAGE")
                                                                  ## [Classical thermodynamics, heat transfer](80-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](80-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](80-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](80-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](80-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](80-04.md "MISSING PAGE")
                                                                                  - [Experimental work](80-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](80-06.md "MISSING PAGE")
                                                                                  - [Thermodynamics and heat transfer](80axx.md "MISSING PAGE")
                                                                                  - [Foundations](80a05.md "MISSING PAGE")
                                                                                  - [Classical thermodynamics, including relativistic](80a10.md "MISSING PAGE")
                                                                                  - [Thermodynamics of continua](80a17.md "MISSING PAGE")
                                                                                  - [Heat and mass transfer, heat flow](80a20.md "MISSING PAGE")
                                                                                  - [Stefan problems, phase changes, etc.](80a22.md "MISSING PAGE")
                                                                                  - [Inverse problems](80a23.md "MISSING PAGE")
                                                                                  - [Combustion](80a25.md "MISSING PAGE")
                                                                                  - [Chemical kinetics](80a30.md "MISSING PAGE")
                                                                                  - [Chemically reacting flows](80a32.md "MISSING PAGE")
                                                                                  - [Chemistry (general)](80a50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](80a99.md "MISSING PAGE")
                                                                                  - [Basic methods](80mxx.md "MISSING PAGE")
                                                                                  - [Finite element methods](80m10.md "MISSING PAGE")
                                                                                  - [Boundary element methods](80m15.md "MISSING PAGE")
                                                                                  - [Finite difference methods](80m20.md "MISSING PAGE")
                                                                                  - [Other numerical methods](80m25.md "MISSING PAGE")
                                                                                  - [Variational methods](80m30.md "MISSING PAGE")
                                                                                  - [Asymptotic analysis](80m35.md "MISSING PAGE")
                                                                                  - [Homogenization](80m40.md "MISSING PAGE")
                                                                                  - [Optimization](80m50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](80m99.md "MISSING PAGE")
                                                                  ## [Quantum theory](81-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](81-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](81-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](81-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](81-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](81-04.md "MISSING PAGE")
                                                                                  - [Experimental papers](81-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](81-06.md "MISSING PAGE")
                                                                                  - [Computational methods](81-08.md "MISSING PAGE")
                                                                                  - [Axiomatics, foundations, philosophy](81pxx.md "MISSING PAGE")
                                                                                  - [General and philosophical](81p05.md "MISSING PAGE")
                                                                                  - [Logical foundations of quantum mechanics; quantum logic](81p10.md "MISSING PAGE")
                                                                                  - [Quantum measurement theory](81p15.md "MISSING PAGE")
                                                                                  - [Stochastic mechanics (including stochastic electrodynamics)](81p20.md "MISSING PAGE")
                                                                                  - [Quantum computation and quantum cryptography](81p68.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81p99.md "MISSING PAGE")
                                                                                  - [General mathematical topics and methods in quantum theory](81qxx.md "MISSING PAGE")
                                                                                  - [Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations](81q05.md "MISSING PAGE")
                                                                                  - [Selfadjoint operator theory in quantum theory, including spectral analysis](81q10.md "MISSING PAGE")
                                                                                  - [Perturbation theories for operators and differential equations](81q15.md "MISSING PAGE")
                                                                                  - [Semiclassical techniques including WKB and Maslov methods](81q20.md "MISSING PAGE")
                                                                                  - [Feynman integrals and graphs; applications of algebraic topology and algebraic geometry](81q30.md "MISSING PAGE")
                                                                                  - [Bethe-Salpeter and other integral equations](81q40.md "MISSING PAGE")
                                                                                  - [Quantum chaos](81q50.md "MISSING PAGE")
                                                                                  - [Supersymmetric quantum mechanics](81q60.md "MISSING PAGE")
                                                                                  - [Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.](81q70.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81q99.md "MISSING PAGE")
                                                                                  - [Groups and algebras in quantum theory](81rxx.md "MISSING PAGE")
                                                                                  - [Finite-dimensional groups and algebras motivated by physics and their representations](81r05.md "MISSING PAGE")
                                                                                  - [Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations](81r10.md "MISSING PAGE")
                                                                                  - [Relations with integrable systems](81r12.md "MISSING PAGE")
                                                                                  - [Operator algebra methods](81r15.md "MISSING PAGE")
                                                                                  - [Covariant wave equations](81r20.md "MISSING PAGE")
                                                                                  - [Spinor and twistor methods](81r25.md "MISSING PAGE")
                                                                                  - [Coherent states; squeezed states](81r30.md "MISSING PAGE")
                                                                                  - [Symmetry breaking](81r40.md "MISSING PAGE")
                                                                                  - [Quantum groups and related algebraic methods](81r50.md "MISSING PAGE")
                                                                                  - [Noncommutative geometry](81r60.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81r99.md "MISSING PAGE")
                                                                                  - [General quantum mechanics and problems of quantization](81sxx.md "MISSING PAGE")
                                                                                  - [Commutation relations and statistics](81s05.md "MISSING PAGE")
                                                                                  - [Geometry and quantization, symplectic methods](81s10.md "MISSING PAGE")
                                                                                  - [Stochastic quantization](81s20.md "MISSING PAGE")
                                                                                  - [Quantum stochastic calculus](81s25.md "MISSING PAGE")
                                                                                  - [Phase space methods including Wigner distributions, etc.](81s30.md "MISSING PAGE")
                                                                                  - [Path integrals](81s40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81s99.md "MISSING PAGE")
                                                                                  - [Quantum field theory; related classical field theories](81txx.md "MISSING PAGE")
                                                                                  - [Axiomatic quantum field theory; operator algebras](81t05.md "MISSING PAGE")
                                                                                  - [Constructive quantum field theory](81t08.md "MISSING PAGE")
                                                                                  - [Model quantum field theories](81t10.md "MISSING PAGE")
                                                                                  - [Yang-Mills and other gauge theories](81t13.md "MISSING PAGE")
                                                                                  - [Perturbative methods of renormalization](81t15.md "MISSING PAGE")
                                                                                  - [Nonperturbative methods of renormalization](81t16.md "MISSING PAGE")
                                                                                  - [Renormalization group methods](81t17.md "MISSING PAGE")
                                                                                  - [Feynman diagrams](81t18.md "MISSING PAGE")
                                                                                  - [Quantum field theory on curved space backgrounds](81t20.md "MISSING PAGE")
                                                                                  - [Quantum field theory on lattices](81t25.md "MISSING PAGE")
                                                                                  - [Continuum limits](81t27.md "MISSING PAGE")
                                                                                  - [String and superstring theories; other extended objects (e.g., branes)](81t30.md "MISSING PAGE")
                                                                                  - [Two-dimensional field theories, conformal field theories, etc.](81t40.md "MISSING PAGE")
                                                                                  - [Topological field theories](81t45.md "MISSING PAGE")
                                                                                  - [Anomalies](81t50.md "MISSING PAGE")
                                                                                  - [Supersymmetric field theories](81t60.md "MISSING PAGE")
                                                                                  - [Quantization in field theory; cohomological methods](81t70.md "MISSING PAGE")
                                                                                  - [Noncommutative geometry methods](81t75.md "MISSING PAGE")
                                                                                  - [Simulation and numerical modeling](81t80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81t99.md "MISSING PAGE")
                                                                                  - [Scattering theory](81uxx.md "MISSING PAGE")
                                                                                  - [$2$-body potential scattering theory](81u05.md "MISSING PAGE")
                                                                                  - [$n$-body potential scattering theory](81u10.md "MISSING PAGE")
                                                                                  - [Exactly and quasi-solvable systems](81u15.md "MISSING PAGE")
                                                                                  - [$S$-matrix theory, etc.](81u20.md "MISSING PAGE")
                                                                                  - [Dispersion theory, dispersion relations](81u30.md "MISSING PAGE")
                                                                                  - [Inverse scattering problems](81u40.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81u99.md "MISSING PAGE")
                                                                                  - [Applications to specific physical systems](81vxx.md "MISSING PAGE")
                                                                                  - [Strong interaction, including quantum chromodynamics](81v05.md "MISSING PAGE")
                                                                                  - [Electromagnetic interaction; quantum electrodynamics](81v10.md "MISSING PAGE")
                                                                                  - [Weak interaction](81v15.md "MISSING PAGE")
                                                                                  - [Gravitational interaction](81v17.md "MISSING PAGE")
                                                                                  - [Other fundamental interactions](81v19.md "MISSING PAGE")
                                                                                  - [Unified theories](81v22.md "MISSING PAGE")
                                                                                  - [Other elementary particle theory](81v25.md "MISSING PAGE")
                                                                                  - [Nuclear physics](81v35.md "MISSING PAGE")
                                                                                  - [Atomic physics](81v45.md "MISSING PAGE")
                                                                                  - [Molecular physics](81v55.md "MISSING PAGE")
                                                                                  - [Many-body theory; quantum Hall effect](81v70.md "MISSING PAGE")
                                                                                  - [Quantum optics](81v80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](81v99.md "MISSING PAGE")
                                                                  ## [Statistical mechanics, structure of matter](82-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](82-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](82-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](82-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](82-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](82-04.md "MISSING PAGE")
                                                                                  - [Experimental papers](82-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](82-06.md "MISSING PAGE")
                                                                                  - [Computational methods](82-08.md "MISSING PAGE")
                                                                                  - [Equilibrium statistical mechanics](82bxx.md "MISSING PAGE")
                                                                                  - [Foundations](82b03.md "MISSING PAGE")
                                                                                  - [Classical equilibrium statistical mechanics (general)](82b05.md "MISSING PAGE")
                                                                                  - [Quantum equilibrium statistical mechanics (general)](82b10.md "MISSING PAGE")
                                                                                  - [Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs](82b20.md "MISSING PAGE")
                                                                                  - [Continuum models (systems of particles, etc.)](82b21.md "MISSING PAGE")
                                                                                  - [Exactly solvable models; Bethe ansatz](82b23.md "MISSING PAGE")
                                                                                  - [Interface problems; diffusion-limited aggregation](82b24.md "MISSING PAGE")
                                                                                  - [Phase transitions (general)](82b26.md "MISSING PAGE")
                                                                                  - [Critical phenomena](82b27.md "MISSING PAGE")
                                                                                  - [Renormalization group methods](82b28.md "MISSING PAGE")
                                                                                  - [Statistical thermodynamics](82b30.md "MISSING PAGE")
                                                                                  - [Stochastic methods](82b31.md "MISSING PAGE")
                                                                                  - [Irreversible thermodynamics, including Onsager-Machlup theory](82b35.md "MISSING PAGE")
                                                                                  - [Kinetic theory of gases](82b40.md "MISSING PAGE")
                                                                                  - [Random walks, random surfaces, lattice animals, etc.](82b41.md "MISSING PAGE")
                                                                                  - [Percolation](82b43.md "MISSING PAGE")
                                                                                  - [Disordered systems (random Ising models, random Schrödinger operators, etc.)](82b44.md "MISSING PAGE")
                                                                                  - [Numerical methods (Monte Carlo, series resummation, etc.)](82b80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](82b99.md "MISSING PAGE")
                                                                                  - [Time-dependent statistical mechanics (dynamic and nonequilibrium)](82cxx.md "MISSING PAGE")
                                                                                  - [Foundations](82c03.md "MISSING PAGE")
                                                                                  - [Classical dynamic and nonequilibrium statistical mechanics (general)](82c05.md "MISSING PAGE")
                                                                                  - [Quantum dynamics and nonequilibrium statistical mechanics (general)](82c10.md "MISSING PAGE")
                                                                                  - [Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs](82c20.md "MISSING PAGE")
                                                                                  - [Dynamic continuum models (systems of particles, etc.)](82c21.md "MISSING PAGE")
                                                                                  - [Interacting particle systems](82c22.md "MISSING PAGE")
                                                                                  - [Exactly solvable dynamic models](82c23.md "MISSING PAGE")
                                                                                  - [Interface problems; diffusion-limited aggregation](82c24.md "MISSING PAGE")
                                                                                  - [Dynamic and nonequilibrium phase transitions (general)](82c26.md "MISSING PAGE")
                                                                                  - [Dynamic critical phenomena](82c27.md "MISSING PAGE")
                                                                                  - [Dynamic renormalization group methods](82c28.md "MISSING PAGE")
                                                                                  - [Stochastic methods (Fokker-Planck, Langevin, etc.)](82c31.md "MISSING PAGE")
                                                                                  - [Neural nets](82c32.md "MISSING PAGE")
                                                                                  - [Irreversible thermodynamics, including Onsager-Machlup theory](82c35.md "MISSING PAGE")
                                                                                  - [Kinetic theory of gases](82c40.md "MISSING PAGE")
                                                                                  - [Dynamics of random walks, random surfaces, lattice animals, etc.](82c41.md "MISSING PAGE")
                                                                                  - [Time-dependent percolation](82c43.md "MISSING PAGE")
                                                                                  - [Dynamics of disordered systems (random Ising systems, etc.)](82c44.md "MISSING PAGE")
                                                                                  - [Transport processes](82c70.md "MISSING PAGE")
                                                                                  - [Numerical methods (Monte Carlo, series resummation, etc.)](82c80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](82c99.md "MISSING PAGE")
                                                                                  - [Applications to specific types of physical systems](82dxx.md "MISSING PAGE")
                                                                                  - [Gases](82d05.md "MISSING PAGE")
                                                                                  - [Plasmas](82d10.md "MISSING PAGE")
                                                                                  - [Liquids](82d15.md "MISSING PAGE")
                                                                                  - [Solids](82d20.md "MISSING PAGE")
                                                                                  - [Crystals](82d25.md "MISSING PAGE")
                                                                                  - [Random media, disordered materials (including liquid crystals and spin glasses)](82d30.md "MISSING PAGE")
                                                                                  - [Metals](82d35.md "MISSING PAGE")
                                                                                  - [Semiconductors](82d37.md "MISSING PAGE")
                                                                                  - [Magnetic materials](82d40.md "MISSING PAGE")
                                                                                  - [Ferroelectrics](82d45.md "MISSING PAGE")
                                                                                  - [Superfluids](82d50.md "MISSING PAGE")
                                                                                  - [Superconductors](82d55.md "MISSING PAGE")
                                                                                  - [Polymers](82d60.md "MISSING PAGE")
                                                                                  - [Nuclear reactor theory; neutron transport](82d75.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](82d99.md "MISSING PAGE")
                                                                  ## [Relativity and gravitational theory](83-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](83-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](83-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](83-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](83-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](83-04.md "MISSING PAGE")
                                                                                  - [Experimental work](83-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](83-06.md "MISSING PAGE")
                                                                                  - [Computational methods](83-08.md "MISSING PAGE")
                                                                                  - [Special relativity](83a05.md "MISSING PAGE")
                                                                                  - [Observational and experimental questions](83b05.md "MISSING PAGE")
                                                                                  - [General relativity](83cxx.md "MISSING PAGE")
                                                                                  - [Einstein's equations (general structure, canonical formalism, Cauchy problems)](83c05.md "MISSING PAGE")
                                                                                  - [Equations of motion](83c10.md "MISSING PAGE")
                                                                                  - [Exact solutions](83c15.md "MISSING PAGE")
                                                                                  - [Classes of solutions; algebraically special solutions, metrics with symmetries](83c20.md "MISSING PAGE")
                                                                                  - [Einstein-Maxwell equations](83c22.md "MISSING PAGE")
                                                                                  - [Approximation procedures, weak fields](83c25.md "MISSING PAGE")
                                                                                  - [Lattice gravity, Regge calculus and other discrete methods](83c27.md "MISSING PAGE")
                                                                                  - [Asymptotic procedures (radiation, news functions, {scr H]-spaces, etc.)](83c30.md "MISSING PAGE")
                                                                                  - [Gravitational waves](83c35.md "MISSING PAGE")
                                                                                  - [Gravitational energy and conservation laws; groups of motions](83c40.md "MISSING PAGE")
                                                                                  - [Quantization of the gravitational field](83c45.md "MISSING PAGE")
                                                                                  - [Methods of quantum field theory](83c47.md "MISSING PAGE")
                                                                                  - [Electromagnetic fields](83c50.md "MISSING PAGE")
                                                                                  - [Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)](83c55.md "MISSING PAGE")
                                                                                  - [Black holes](83c57.md "MISSING PAGE")
                                                                                  - [Spinor and twistor methods; Newman-Penrose formalism](83c60.md "MISSING PAGE")
                                                                                  - [Methods of noncommutative geometry](83c65.md "MISSING PAGE")
                                                                                  - [Space-time singularities, cosmic censorship, etc.](83c75.md "MISSING PAGE")
                                                                                  - [Analogues in lower dimensions](83c80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](83c99.md "MISSING PAGE")
                                                                                  - [Relativistic gravitational theories other than Einstein's, including asymmetric field theories](83d05.md "MISSING PAGE")
                                                                                  - [Unified, higher-dimensional and super field theories](83exx.md "MISSING PAGE")
                                                                                  - [Geometrodynamics](83e05.md "MISSING PAGE")
                                                                                  - [Kaluza-Klein and other higher-dimensional theories](83e15.md "MISSING PAGE")
                                                                                  - [String and superstring theories](83e30.md "MISSING PAGE")
                                                                                  - [Supergravity](83e50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](83e99.md "MISSING PAGE")
                                                                                  - [Cosmology](83f05.md "MISSING PAGE")
                                                                                  - [Astronomy and astrophysics](85-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](85-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](85-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](85-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](85-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](85-04.md "MISSING PAGE")
                                                                                  - [Experimental work](85-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](85-06.md "MISSING PAGE")
                                                                                  - [Computational methods](85-08.md "MISSING PAGE")
                                                                                  - [General](85a04.md "MISSING PAGE")
                                                                                  - [Galactic and stellar dynamics](85a05.md "MISSING PAGE")
                                                                                  - [Galactic and stellar structure](85a15.md "MISSING PAGE")
                                                                                  - [Planetary atmospheres](85a20.md "MISSING PAGE")
                                                                                  - [Radiative transfer](85a25.md "MISSING PAGE")
                                                                                  - [Hydrodynamic and hydromagnetic problems](85a30.md "MISSING PAGE")
                                                                                  - [Statistical astronomy](85a35.md "MISSING PAGE")
                                                                                  - [Cosmology](85a40.md "MISSING PAGE")
                                                                                  - [Miscellaneous topics](85a99.md "MISSING PAGE")
                                                                                  - [Geophysics](86-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](86-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](86-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](86-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](86-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](86-04.md "MISSING PAGE")
                                                                                  - [Experimental work](86-05.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](86-06.md "MISSING PAGE")
                                                                                  - [Computational methods](86-08.md "MISSING PAGE")
                                                                                  - [General](86a04.md "MISSING PAGE")
                                                                                  - [Hydrology, hydrography, oceanography](86a05.md "MISSING PAGE")
                                                                                  - [Meteorology and atmospheric physics](86a10.md "MISSING PAGE")
                                                                                  - [Seismology](86a15.md "MISSING PAGE")
                                                                                  - [Global dynamics, earthquake problems](86a17.md "MISSING PAGE")
                                                                                  - [Potentials, prospecting](86a20.md "MISSING PAGE")
                                                                                  - [Inverse problems](86a22.md "MISSING PAGE")
                                                                                  - [Geo-electricity and geomagnetism](86a25.md "MISSING PAGE")
                                                                                  - [Geodesy, mapping problems](86a30.md "MISSING PAGE")
                                                                                  - [Geostatistics](86a32.md "MISSING PAGE")
                                                                                  - [Glaciology](86a40.md "MISSING PAGE")
                                                                                  - [Geological problems](86a60.md "MISSING PAGE")
                                                                                  - [Miscellaneous topics](86a99.md "MISSING PAGE")
                                                                  ## [Operations research, mathematical programming](90-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](90-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](90-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](90-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](90-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](90-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](90-06.md "MISSING PAGE")
                                                                                  - [Computational methods](90-08.md "MISSING PAGE")
                                                                                  - [Operations research and management science](90bxx.md "MISSING PAGE")
                                                                                  - [Inventory, storage, reservoirs](90b05.md "MISSING PAGE")
                                                                                  - [Transportation, logistics](90b06.md "MISSING PAGE")
                                                                                  - [Network models, deterministic](90b10.md "MISSING PAGE")
                                                                                  - [Network models, stochastic](90b15.md "MISSING PAGE")
                                                                                  - [Communication networks](90b18.md "MISSING PAGE")
                                                                                  - [Traffic problems](90b20.md "MISSING PAGE")
                                                                                  - [Queues and service](90b22.md "MISSING PAGE")
                                                                                  - [Reliability, availability, maintenance, inspection](90b25.md "MISSING PAGE")
                                                                                  - [Production models](90b30.md "MISSING PAGE")
                                                                                  - [Scheduling theory, deterministic](90b35.md "MISSING PAGE")
                                                                                  - [Scheduling theory, stochastic](90b36.md "MISSING PAGE")
                                                                                  - [Search theory](90b40.md "MISSING PAGE")
                                                                                  - [Management decision making, including multiple objectives](90b50.md "MISSING PAGE")
                                                                                  - [Marketing, advertising](90b60.md "MISSING PAGE")
                                                                                  - [Theory of organizations, manpower planning](90b70.md "MISSING PAGE")
                                                                                  - [Discrete location and assignment](90b80.md "MISSING PAGE")
                                                                                  - [Continuous location](90b85.md "MISSING PAGE")
                                                                                  - [Case-oriented studies](90b90.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](90b99.md "MISSING PAGE")
                                                                                  - [Mathematical programming](90cxx.md "MISSING PAGE")
                                                                                  - [Linear programming](90c05.md "MISSING PAGE")
                                                                                  - [Large-scale problems](90c06.md "MISSING PAGE")
                                                                                  - [Special problems of linear programming (transportation, multi-index, etc.)](90c08.md "MISSING PAGE")
                                                                                  - [Boolean programming](90c09.md "MISSING PAGE")
                                                                                  - [Integer programming](90c10.md "MISSING PAGE")
                                                                                  - [Mixed integer programming](90c11.md "MISSING PAGE")
                                                                                  - [Stochastic programming](90c15.md "MISSING PAGE")
                                                                                  - [Quadratic programming](90c20.md "MISSING PAGE")
                                                                                  - [Semidefinite programming](90c22.md "MISSING PAGE")
                                                                                  - [Convex programming](90c25.md "MISSING PAGE")
                                                                                  - [Nonconvex programming](90c26.md "MISSING PAGE")
                                                                                  - [Combinatorial optimization](90c27.md "MISSING PAGE")
                                                                                  - [Multi-objective and goal programming](90c29.md "MISSING PAGE")
                                                                                  - [Nonlinear programming](90c30.md "MISSING PAGE")
                                                                                  - [Sensitivity, stability, parametric optimization](90c31.md "MISSING PAGE")
                                                                                  - [Fractional programming](90c32.md "MISSING PAGE")
                                                                                  - [Complementarity problems](90c33.md "MISSING PAGE")
                                                                                  - [Semi-infinite programming](90c34.md "MISSING PAGE")
                                                                                  - [Programming involving graphs or networks](90c35.md "MISSING PAGE")
                                                                                  - [Dynamic programming](90c39.md "MISSING PAGE")
                                                                                  - [Markov and semi-Markov decision processes](90c40.md "MISSING PAGE")
                                                                                  - [Optimality conditions, duality](90c46.md "MISSING PAGE")
                                                                                  - [Minimax problems](90c47.md "MISSING PAGE")
                                                                                  - [Programming in abstract spaces](90c48.md "MISSING PAGE")
                                                                                  - [Extreme-point and pivoting methods](90c49.md "MISSING PAGE")
                                                                                  - [Interior-point methods](90c51.md "MISSING PAGE")
                                                                                  - [Methods of reduced gradient type](90c52.md "MISSING PAGE")
                                                                                  - [Methods of quasi-Newton type](90c53.md "MISSING PAGE")
                                                                                  - [Methods of successive quadratic programming type](90c55.md "MISSING PAGE")
                                                                                  - [Derivative-free methods](90c56.md "MISSING PAGE")
                                                                                  - [Polyhedral combinatorics, branch-and-bound, branch-and-cut](90c57.md "MISSING PAGE")
                                                                                  - [Approximation methods and heuristics](90c59.md "MISSING PAGE")
                                                                                  - [Abstract computational complexity for mathematical programming problems](90c60.md "MISSING PAGE")
                                                                                  - [Fuzzy programming](90c70.md "MISSING PAGE")
                                                                                  - [Applications of mathematical programming](90c90.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](90c99.md "MISSING PAGE")
                                                                  ## [Game theory, economics, social and behavioral sciences](91-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](91-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](91-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](91-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from section 01)](91-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](91-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](91-06.md "MISSING PAGE")
                                                                                  - [Computational methods](91-08.md "MISSING PAGE")
                                                                                  - [Game theory](91axx.md "MISSING PAGE")
                                                                                  - [2-person games](91a05.md "MISSING PAGE")
                                                                                  - [$n$-person games, $n>2$](91a06.md "MISSING PAGE")
                                                                                  - [Noncooperative games](91a10.md "MISSING PAGE")
                                                                                  - [Cooperative games](91a12.md "MISSING PAGE")
                                                                                  - [Games with infinitely many players](91a13.md "MISSING PAGE")
                                                                                  - [Stochastic games](91a15.md "MISSING PAGE")
                                                                                  - [Games in extensive form](91a18.md "MISSING PAGE")
                                                                                  - [Multistage and repeated games](91a20.md "MISSING PAGE")
                                                                                  - [Evolutionary games](91a22.md "MISSING PAGE")
                                                                                  - [Differential games](91a23.md "MISSING PAGE")
                                                                                  - [Positional games (pursuit and evasion, etc.)](91a24.md "MISSING PAGE")
                                                                                  - [Dynamic games](91a25.md "MISSING PAGE")
                                                                                  - [Rationality, learning](91a26.md "MISSING PAGE")
                                                                                  - [Signaling, communication](91a28.md "MISSING PAGE")
                                                                                  - [Utility theory for games](91a30.md "MISSING PAGE")
                                                                                  - [Decision theory for games](91a35.md "MISSING PAGE")
                                                                                  - [Game-theoretic models](91a40.md "MISSING PAGE")
                                                                                  - [Games involving graphs](91a43.md "MISSING PAGE")
                                                                                  - [Games involving topology or set theory](91a44.md "MISSING PAGE")
                                                                                  - [Combinatorial games](91a46.md "MISSING PAGE")
                                                                                  - [Discrete-time games](91a50.md "MISSING PAGE")
                                                                                  - [Games of timing](91a55.md "MISSING PAGE")
                                                                                  - [Probabilistic games; gambling](91a60.md "MISSING PAGE")
                                                                                  - [Hierarchical games](91a65.md "MISSING PAGE")
                                                                                  - [Spaces of games](91a70.md "MISSING PAGE")
                                                                                  - [Applications of game theory](91a80.md "MISSING PAGE")
                                                                                  - [Experimental studies](91a90.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](91a99.md "MISSING PAGE")
                                                                                  - [Mathematical economics](91bxx.md "MISSING PAGE")
                                                                                  - [Fundamental topics (basic mathematics, methodology; applicable to economics in general)](91b02.md "MISSING PAGE")
                                                                                  - [Decision theory](91b06.md "MISSING PAGE")
                                                                                  - [Individual preferences](91b08.md "MISSING PAGE")
                                                                                  - [Group preferences](91b10.md "MISSING PAGE")
                                                                                  - [Voting theory](91b12.md "MISSING PAGE")
                                                                                  - [Social choice](91b14.md "MISSING PAGE")
                                                                                  - [Utility theory](91b16.md "MISSING PAGE")
                                                                                  - [Public goods](91b18.md "MISSING PAGE")
                                                                                  - [Price theory and market structure](91b24.md "MISSING PAGE")
                                                                                  - [Market models (auctions, bargaining, bidding, selling, etc.)](91b26.md "MISSING PAGE")
                                                                                  - [Finance, portfolios, investment](91b28.md "MISSING PAGE")
                                                                                  - [Risk theory, insurance](91b30.md "MISSING PAGE")
                                                                                  - [Resource and cost allocation](91b32.md "MISSING PAGE")
                                                                                  - [Production theory, theory of the firm](91b38.md "MISSING PAGE")
                                                                                  - [Labor market, contracts](91b40.md "MISSING PAGE")
                                                                                  - [Consumer behavior, demand theory](91b42.md "MISSING PAGE")
                                                                                  - [Informational economics](91b44.md "MISSING PAGE")
                                                                                  - [Equilibrium: general theory](91b50.md "MISSING PAGE")
                                                                                  - [Special types of equilibria](91b52.md "MISSING PAGE")
                                                                                  - [Special types of economies](91b54.md "MISSING PAGE")
                                                                                  - [General economic models, trade models](91b60.md "MISSING PAGE")
                                                                                  - [Dynamic economic models, growth models](91b62.md "MISSING PAGE")
                                                                                  - [Macro-economic models (monetary models, models of taxation)](91b64.md "MISSING PAGE")
                                                                                  - [Multisectoral models](91b66.md "MISSING PAGE")
                                                                                  - [Matching models](91b68.md "MISSING PAGE")
                                                                                  - [Stochastic models](91b70.md "MISSING PAGE")
                                                                                  - [Spatial models](91b72.md "MISSING PAGE")
                                                                                  - [Models of real-world systems](91b74.md "MISSING PAGE")
                                                                                  - [Environmental economics (natural resource models, harvesting, pollution, etc.)](91b76.md "MISSING PAGE")
                                                                                  - [Statistical methods; economic indices and measures](91b82.md "MISSING PAGE")
                                                                                  - [Economic time series analysis](91b84.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](91b99.md "MISSING PAGE")
                                                                                  - [Social and behavioral sciences: general topics](91cxx.md "MISSING PAGE")
                                                                                  - [Measurement theory](91c05.md "MISSING PAGE")
                                                                                  - [One- and multidimensional scaling](91c15.md "MISSING PAGE")
                                                                                  - [Clustering](91c20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](91c99.md "MISSING PAGE")
                                                                                  - [Mathematical sociology (including anthropology)](91dxx.md "MISSING PAGE")
                                                                                  - [Models of societies, social and urban evolution](91d10.md "MISSING PAGE")
                                                                                  - [Mathematical geography and demography](91d20.md "MISSING PAGE")
                                                                                  - [Spatial models](91d25.md "MISSING PAGE")
                                                                                  - [Social networks](91d30.md "MISSING PAGE")
                                                                                  - [Manpower systems](91d35.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](91d99.md "MISSING PAGE")
                                                                                  - [Mathematical psychology](91exx.md "MISSING PAGE")
                                                                                  - [Cognitive psychology](91e10.md "MISSING PAGE")
                                                                                  - [Psychophysics and psychophysiology; perception](91e30.md "MISSING PAGE")
                                                                                  - [Memory and learning](91e40.md "MISSING PAGE")
                                                                                  - [Measurement and performance](91e45.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](91e99.md "MISSING PAGE")
                                                                                  - [Other social and behavioral sciences (mathematical treatment)](91fxx.md "MISSING PAGE")
                                                                                  - [History, political science](91f10.md "MISSING PAGE")
                                                                                  - [Linguistics](91f20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](91f99.md "MISSING PAGE")
                                                                  ## [Biology and other natural sciences](92-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](92-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](92-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](92-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](92-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](92-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](92-06.md "MISSING PAGE")
                                                                                  - [Computational methods](92-08.md "MISSING PAGE")
                                                                                  - [Mathematical biology in general](92bxx.md "MISSING PAGE")
                                                                                  - [General biology and biomathematics](92b05.md "MISSING PAGE")
                                                                                  - [Taxonomy, statistics](92b10.md "MISSING PAGE")
                                                                                  - [General biostatistics](92b15.md "MISSING PAGE")
                                                                                  - [Neural networks, artificial life and related topics](92b20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](92b99.md "MISSING PAGE")
                                                                                  - [Physiological, cellular and medical topics](92cxx.md "MISSING PAGE")
                                                                                  - [Biophysics](92c05.md "MISSING PAGE")
                                                                                  - [Biomechanics](92c10.md "MISSING PAGE")
                                                                                  - [Developmental biology, pattern formation](92c15.md "MISSING PAGE")
                                                                                  - [Cell movement (chemotaxis, etc.)](92c17.md "MISSING PAGE")
                                                                                  - [Neural biology](92c20.md "MISSING PAGE")
                                                                                  - [Physiology (general)](92c30.md "MISSING PAGE")
                                                                                  - [Physiological flow](92c35.md "MISSING PAGE")
                                                                                  - [Cell biology](92c37.md "MISSING PAGE")
                                                                                  - [Biochemistry, molecular biology](92c40.md "MISSING PAGE")
                                                                                  - [Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)](92c45.md "MISSING PAGE")
                                                                                  - [Medical applications (general)](92c50.md "MISSING PAGE")
                                                                                  - [Biomedical imaging and signal processing](92c55.md "MISSING PAGE")
                                                                                  - [Medical epidemiology](92c60.md "MISSING PAGE")
                                                                                  - [Plant biology](92c80.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](92c99.md "MISSING PAGE")
                                                                                  - [Genetics and population dynamics](92dxx.md "MISSING PAGE")
                                                                                  - [Genetics](92d10.md "MISSING PAGE")
                                                                                  - [Problems related to evolution](92d15.md "MISSING PAGE")
                                                                                  - [Protein sequences, DNA sequences](92d20.md "MISSING PAGE")
                                                                                  - [Population dynamics (general)](92d25.md "MISSING PAGE")
                                                                                  - [Epidemiology](92d30.md "MISSING PAGE")
                                                                                  - [Ecology](92d40.md "MISSING PAGE")
                                                                                  - [Animal behavior](92d50.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](92d99.md "MISSING PAGE")
                                                                                  - [Chemistry](92exx.md "MISSING PAGE")
                                                                                  - [Molecular structure (graph-theoretic methods, methods of differential topology, etc.)](92e10.md "MISSING PAGE")
                                                                                  - [Classical flows, reactions, etc.](92e20.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](92e99.md "MISSING PAGE")
                                                                                  - [Other natural sciences](92f05.md "MISSING PAGE")
                                                                                  - [Systems theory; control](93-xx.md "MISSING PAGE")
                                                                                  - [General reference works (handbooks, dictionaries, bibliographies, etc.)](93-00.md "MISSING PAGE")
                                                                                  - [Instructional exposition (textbooks, tutorial papers, etc.)](93-01.md "MISSING PAGE")
                                                                                  - [Research exposition (monographs, survey articles)](93-02.md "MISSING PAGE")
                                                                                  - [Historical (must also be assigned at least one classification number from Section 01)](93-03.md "MISSING PAGE")
                                                                                  - [Explicit machine computation and programs (not the theory of computation or programming)](93-04.md "MISSING PAGE")
                                                                                  - [Proceedings, conferences, collections, etc.](93-06.md "MISSING PAGE")
                                                                  ## [General](93axx.md "MISSING PAGE")
                                                                                  - [Axiomatic system theory](93a05.md "MISSING PAGE")
                                                                                  - [General systems](93a10.md "MISSING PAGE")
                                                                                  - [Hierarchical systems](93a13.md "MISSING PAGE")
                                                                                  - [Decentralized systems](93a14.md "MISSING PAGE")
                                                                                  - [Large scale systems](93a15.md "MISSING PAGE")
                                                                                  - [Mathematical modeling (models of systems, model-matching, etc.)](93a30.md "MISSING PAGE")
                                                                                  - [None of the above, but in this section](93a99.md "MISSING PAGE")
                                                                                  - [Controllability, observability, and system structure](93bxx.md "MISSING PAGE")
                                                                                  - [Attainable sets](93b03.md "MISSING PAGE")
                                                                                  - [Controllability](93b05.md "MISSING PAGE")
                                                                                  - [Observability](93b07.md "MISSING PAGE")
                                                                                  - [Canonical structure](93b10.md "MISSING PAGE")
                                                                                  - [System structure simplification](93b11.md "MISSING PAGE")
                                                                                  - [Variable structure systems](93b12.md "MISSING PAGE")
                                                                                  - [Realizations from input-output data](93b15.md "MISSING PAGE")
                                                                                  - [Transformations](93b17.md "MISSING PAGE")
                                                                                  - [Linearizations](93b18.md "MISSING PAGE")
                                                                                  - [Minimal systems representations](93b20.md "MISSING PAGE")
                                                                                  - [Algebraic methods](93b25.md "MISSING PAGE")
                                                                                  - [Geometric methods (including algebro-geometric)](93b27.md "MISSING PAGE")
                                                                                  - [Operator-theoretic methods](93b28.md "MISSING PAGE")
                                                                                  - [Differential-geometric methods](93b29.md "MISSING PAGE")
                                                                                  - [System identification](93b30.md "MISSING PAGE")
                                                                                  - [Sensitivity (robustness)](93b35.md "MISSING PAGE")
                                                                                  - [H]^infty$-control](93b36.md "MISSING PAGE")
                                                                                    [Computational methods](93b40.md "MISSING PAGE")
                                                                                    [Synthesis problems](93b50.md "MISSING PAGE")
                                                                                    [Design techniques (robust design, computer-aided design, etc.)](93b51.md "MISSING PAGE")
                                                                                    [Feedback control](93b52.md "MISSING PAGE")
                                                                                    [Pole and zero placement problems](93b55.md "MISSING PAGE")
                                                                                    [Eigenvalue problems](93b60.md "MISSING PAGE")
                                                                                    [None of the above, but in this section](93b99.md "MISSING PAGE")
                                                                                    [Control systems, guided systems](93cxx.md "MISSING PAGE")
                                                                                    [Linear systems](93c05.md "MISSING PAGE")
                                                                                    [Nonlinear systems](93c10.md "MISSING PAGE")
                                                                                    [Systems governed by ordinary differential equations](93c15.md "MISSING PAGE")
                                                                                    [Systems governed by partial differential equations](93c20.md "MISSING PAGE")
                                                                                    [Systems governed by functional-differential equations](93c23.md "MISSING PAGE")
                                                                                    [Systems in abstract spaces](93c25.md "MISSING PAGE")
                                                                                    [Systems governed by functional relations other than differential equations](93c30.md "MISSING PAGE")
                                                                                    [Multivariable systems](93c35.md "MISSING PAGE")
                                                                                    [Adaptive control](93c40.md "MISSING PAGE")
                                                                                    [Problems with incomplete information](93c41.md "MISSING PAGE")
                                                                                    [Fuzzy control](93c42.md "MISSING PAGE")
                                                                                    [Discrete-time systems](93c55.md "MISSING PAGE")
                                                                                    [Sampled-data systems](93c57.md "MISSING PAGE")
                                                                                    [Digital systems](93c62.md "MISSING PAGE")
                                                                                    [Discrete event systems](93c65.md "MISSING PAGE")
                                                                                    [Time-scale analysis and singular perturbations](93c70.md "MISSING PAGE")
                                                                                    [Perturbations](93c73.md "MISSING PAGE")
                                                                                    [Frequency-response methods](93c80.md "MISSING PAGE")
                                                                                    [Control problems involving computers (process control, etc.)](93c83.md "MISSING PAGE")
                                                                                    [Automated systems (robots, etc.)](93c85.md "MISSING PAGE")
                                                                                    [Applications](93c95.md "MISSING PAGE")
                                                                                    [None of the above, but in this section](93c99.md "MISSING PAGE")
                                                                                    [Stability](93dxx.md "MISSING PAGE")
                                                                                    [Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)](93d05.md "MISSING PAGE")
                                                                                    [Robust stability](93d09.md "MISSING PAGE")
                                                                                    [Popov-type stability of feedback systems](93d10.md "MISSING PAGE")
                                                                                    [Stabilization of systems by feedback](93d15.md "MISSING PAGE")
                                                                                    [Asymptotic stability](93d20.md "MISSING PAGE")
                                                                                    [Adaptive or robust stabilization](93d21.md "MISSING PAGE")
                                                                                    [Input-output approaches](93d25.md "MISSING PAGE")
                                                                                    [Scalar and vector Lyapunov functions](93d30.md "MISSING PAGE")
                                                                                    [None of the above, but in this section](93d99.md "MISSING PAGE")
                                                                                    [Stochastic systems and control](93exx.md "MISSING PAGE")
                                                                                    [Stochastic systems, general](93e03.md "MISSING PAGE")
                                                                                    [Estimation and detection](93e10.md "MISSING PAGE")
                                                                                    [Filtering](93e11.md "MISSING PAGE")
                                                                                    [System identification](93e12.md "MISSING PAGE")
                                                                                    [Data smoothing](93e14.md "MISSING PAGE")
                                                                                    [Stochastic stability](93e15.md "MISSING PAGE")
                                                                                    [Optimal stochastic control](93e20.md "MISSING PAGE")
                                                                                    [Least squares and related methods](93e24.md "MISSING PAGE")
                                                                                    [Other computational methods](93e25.md "MISSING PAGE")
                                                                                    [Stochastic learning and adaptive control](93e35.md "MISSING PAGE")
                                                                                    [None of the above, but in this section](93e99.md "MISSING PAGE")
                                                                                    [Information and communication, circuits](94-xx.md "MISSING PAGE")
                                                                                    [General reference works (handbooks, dictionaries, bibliographies, etc.)](94-00.md "MISSING PAGE")
                                                                                    [Instructional exposition (textbooks, tutorial papers, etc.)](94-01.md "MISSING PAGE")
                                                                                    [Research exposition (monographs, survey articles)](94-02.md "MISSING PAGE")
                                                                                    [Historical (must also be assigned at least one classification number from Section 01)](94-03.md "MISSING PAGE")
                                                                                    [Explicit machine computation and programs (not the theory of computation or programming)](94-04.md "MISSING PAGE")
                                                                                    [Proceedings, conferences, collections, etc.](94-06.md "MISSING PAGE")
                                                                                  - ## [Communication, information](94axx.md "MISSING PAGE")
                                                                                  - - [Communication theory](94a05.md "MISSING PAGE")
                                                                                                      - [Image processing (compression, reconstruction, etc.)](94a08.md "MISSING PAGE")
                                                                                                      - [Application of orthogonal functions in communication](94a11.md "MISSING PAGE")
                                                                                                      - [Signal theory (characterization, reconstruction, etc.)](94a12.md "MISSING PAGE")
                                                                                                      - [Detection theory](94a13.md "MISSING PAGE")
                                                                                                      - [Modulation and demodulation](94a14.md "MISSING PAGE")
                                                                                                      - [Information theory, general](94a15.md "MISSING PAGE")
                                                                                                      - [Measures of information, entropy](94a17.md "MISSING PAGE")
                                                                                                      - [Sampling theory](94a20.md "MISSING PAGE")
                                                                                                      - [Coding theorems (Shannon theory)](94a24.md "MISSING PAGE")
                                                                                                      - [Source coding](94a29.md "MISSING PAGE")
                                                                                                      - [Rate-distortion theory](94a34.md "MISSING PAGE")
                                                                                                      - [Channel models](94a40.md "MISSING PAGE")
                                                                                                      - [Prefix, length-variable, comma-free codes](94a45.md "MISSING PAGE")
                                                                                                      - [Theory of questionnaires](94a50.md "MISSING PAGE")
                                                                                                      - [Shift register sequences and sequences over finite alphabets](94a55.md "MISSING PAGE")
                                                                                                      - [Cryptography](94a60.md "MISSING PAGE")
                                                                                                      - [Authentication and secret sharing](94a62.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](94a99.md "MISSING PAGE")
                                                                                                      - [Theory of error-correcting codes and error-detecting codes](94bxx.md "MISSING PAGE")
                                                                                                      - [Linear codes, general](94b05.md "MISSING PAGE")
                                                                                                      - [Convolutional codes](94b10.md "MISSING PAGE")
                                                                                                      - [Combined modulation schemes (including trellis codes)](94b12.md "MISSING PAGE")
                                                                                                      - [Cyclic codes](94b15.md "MISSING PAGE")
                                                                                                      - [Burst-correcting codes](94b20.md "MISSING PAGE")
                                                                                                      - [Combinatorial codes](94b25.md "MISSING PAGE")
                                                                                                      - [Geometric methods (including applications of algebraic geometry)](94b27.md "MISSING PAGE")
                                                                                                      - [Majority codes](94b30.md "MISSING PAGE")
                                                                                                      - [Decoding](94b35.md "MISSING PAGE")
                                                                                                      - [Arithmetic codes](94b40.md "MISSING PAGE")
                                                                                                      - [Synchronization error-correcting codes](94b50.md "MISSING PAGE")
                                                                                                      - [Other types of codes](94b60.md "MISSING PAGE")
                                                                                                      - [Bounds on codes](94b65.md "MISSING PAGE")
                                                                                                      - [Error probability](94b70.md "MISSING PAGE")
                                                                                                      - [Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)](94b75.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](94b99.md "MISSING PAGE")
                                                                                                      - [Circuits, networks](94cxx.md "MISSING PAGE")
                                                                                                      - [Analytic circuit theory](94c05.md "MISSING PAGE")
                                                                                                      - [Switching theory, application of Boolean algebra; Boolean functions](94c10.md "MISSING PAGE")
                                                                                                      - [Fault detection; testing](94c12.md "MISSING PAGE")
                                                                                                      - [Applications of graph theory](94c15.md "MISSING PAGE")
                                                                                                      - [Applications of design theory](94c30.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](94c99.md "MISSING PAGE")
                                                                                                      - [Fuzzy sets and logic (in connection with questions of Section 94)](94d05.md "MISSING PAGE")
                                                                                  - ## [Mathematics education](97-xx.md "MISSING PAGE")
                                                                                  - - [General reference works (handbooks, dictionaries, bibliographies, etc.)](97-00.md "MISSING PAGE")
                                                                                                      - [Instructional exposition (textbooks, tutorial papers, etc.)](97-01.md "MISSING PAGE")
                                                                                                      - [Research exposition (monographs, survey articles)](97-02.md "MISSING PAGE")
                                                                                                      - [Historical (must also be assigned at least one classification number from Section 01)](97-03.md "MISSING PAGE")
                                                                                                      - [Explicit machine computation and programs (not the theory of computation or programming)](97-04.md "MISSING PAGE")
                                                                                                      - [Proceedings, conferences, collections, etc.](97-06.md "MISSING PAGE")
                                                                                                      - [General](97axx.md "MISSING PAGE")
                                                                                                      - [Recreational mathematics](97a20.md "MISSING PAGE")
                                                                                                      - [Sociological issues](97a40.md "MISSING PAGE")
                                                                                                      - [Standards](97a80.md "MISSING PAGE")
                                                                                                      - [Fiction and games](97a90.md "MISSING PAGE")
                                                                                                      - [Educational policy and educational systems](97bxx.md "MISSING PAGE")
                                                                                                      - [Educational research and planning](97b10.md "MISSING PAGE")
                                                                                                      - [General education](97b20.md "MISSING PAGE")
                                                                                                      - [Vocational education](97b30.md "MISSING PAGE")
                                                                                                      - [Higher education](97b40.md "MISSING PAGE")
                                                                                                      - [Teacher education](97b50.md "MISSING PAGE")
                                                                                                      - [Out-of-school education. Adult and further education](97b60.md "MISSING PAGE")
                                                                                                      - [Syllabuses. Curriculum guides, official documents](97b70.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](97b99.md "MISSING PAGE")
                                                                                                      - [Psychology of and research in mathematics education](97cxx.md "MISSING PAGE")
                                                                                                      - [Affective aspects (motivation, anxiety, persistence, etc.)](97c20.md "MISSING PAGE")
                                                                                                      - [Student learning and thinking (misconceptions, cognitive development, problem solving, etc.)](97c30.md "MISSING PAGE")
                                                                                                      - [Assessment (large scale assessment, validity, reliability, etc.)](97c40.md "MISSING PAGE")
                                                                                                      - [Theoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.)](97c50.md "MISSING PAGE")
                                                                                                      - [Sociological aspects of learning (culture, group interactions, equity issues, etc.)](97c60.md "MISSING PAGE")
                                                                                                      - [Teachers, and research on teacher education (teacher development, etc.)](97c70.md "MISSING PAGE")
                                                                                                      - [Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.)](97c80.md "MISSING PAGE")
                                                                                                      - [Teaching and curriculum (innovations, teaching practices, studies of curriculum materials, effective teaching, etc. )](97c90.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](97c99.md "MISSING PAGE")
                                                                                                      - [Education and instruction in mathematics](97dxx.md "MISSING PAGE")
                                                                                                      - [Comparative studies on mathematics education](97d10.md "MISSING PAGE")
                                                                                                      - [Philosophical and theoretical contributions to mathematical education](97d20.md "MISSING PAGE")
                                                                                                      - [Goals of mathematics teaching. Curriculum development](97d30.md "MISSING PAGE")
                                                                                                      - [Teaching methods and classroom techniques. Lesson preparation. Educational principles](97d40.md "MISSING PAGE")
                                                                                                      - [Teaching problem solving and heuristic strategies](97d50.md "MISSING PAGE")
                                                                                                      - [Achievement control and rating](97d60.md "MISSING PAGE")
                                                                                                      - [Diagnosis, analysis and remediation of learning difficulties and student errors](97d70.md "MISSING PAGE")
                                                                                                      - [Teaching units, draft lessons and master lessons](97d80.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](97d99.md "MISSING PAGE")
                                                                                                      - [Educational material and media. Educational technology](97uxx.md "MISSING PAGE")
                                                                                                      - [Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom](97u20.md "MISSING PAGE")
                                                                                                      - [Teacher manuals and planning aids](97u30.md "MISSING PAGE")
                                                                                                      - [Problem books; student competitions, examination questions](97u40.md "MISSING PAGE")
                                                                                                      - [Computer assisted instruction and programmed instruction](97u50.md "MISSING PAGE")
                                                                                                      - [Manipulative materials and their use in the classroom](97u60.md "MISSING PAGE")
                                                                                                      - [Technological tools (computers, calculators, software, etc.) and their use in the classroom](97u70.md "MISSING PAGE")
                                                                                                      - [Audiovisual media and their use in instruction](97u80.md "MISSING PAGE")
                                                                                                      - [None of the above, but in this section](97u99.md "MISSING PAGE")